The Carter administration is beginning its final round of planning for next January's economic policies in just the kind of box it has sought all year to avoid: It's faced with the prospect of a sluggish economy, but can't do much about it because of the need to slow inflation. At the same time, no one really knows how to slow inflation very effectively.

When Carter announced his 1978 economic program last January, there was a good deal of optimism both in and outside the government. After a year of bumbling and overpromising, the administration was about to get its act together - with more measured, conventional proposals. The economy seemed robust enough. And although inflation was worrisome, it seemed unlikely to speed up much.

Now, as the administration prepares for its January budget and economic proposals, most of these goals still seem elusive, the inflation outlook has worsened visibly, the tax-reduction and "reform" bill the president proposed has been reshaped by Congress into a high-income relief measure that he now is threatening to veto, his wage-price program is foundering and the dollar is in a slump.

The main bright spot has been that the unemployment rate has dropped far more sharply than had been predicted - from 7 percent at this time a year ago to 5.9 percent in August - despite a hefty increase in the number of persons seeking jobs. But even this almost entirely unexpected event has virtually been overshadowed by mounting concern over the inflation rate and the sinking dollar.

Moreover, while talk of a recession next year has dimmed in recent weeks, one still is possible - and, at the least, most analysts still are predicting below-par growth for the bulk of 1979. Opinion polls show voters already lack confidence in the president's ability to deal with economic problems. Some say the pocketbook issue could help defeat Carter in 1980.

The problem is compounded by the realization that, this time at least, there are no easy solutions. Economists concede frankly they are don't know how to deal with Carter's most critical issue - worsening inflation - and the White House task force assigned to develop a program previously plowed ground.

How did the administration get into such a fix - again?

The answers are complex ones, and often interrelated:

Along with economists outside government, the administration's top policy makers grossly underestimated the worsening inflation - and began serious moves to cope with it too late. Carter's latest anti-inflation efforts last January were regarded as token, even by the White House. The intensity of the wage-price surge surprised everyone - including Carter.

White House ineptitude in dealing with Congress has led to delay and revamping of much of Carter's major tax cut and energy legislation - with the result that the measures will have far less impact.For example, no one doubts now that some reduction in taxes will be enacted. But the likelihood is it will be too small - and too late - to do more than prevent a more serious slowdown.

Critics charge that Carter also has failed to exercise serious discipline on the budget side, relying on re-estimates and spending shortfalls to bail him out. Complains GOP economist Murray L. Weidenbaum: "Any real restraint has come entirely by accident." Carter's first major veto came last month, on a defense bill. As a result, his veto threats today are largely discounted.

In part because of the administration's failure to cope with the energy and inflation problems, the dollar has been buffeted in the foreign exchange markets - adding to problems here at home. The dollar slide not only exacerbates inflation in the U.S., it also heightens pressure on the government to slow the economy - a move Carter had not wanted to make.

The worsening inflation - and now, the continuing dollar slide - has forced the Federal Reserve Board to boost interest rates sharply, heightening the danger of a recession. Moreover, contrary to what officials had hoped earlier this year, the Fed's tightening is not expected to end soon. Because of the dollar crunch, interest rates may remain high for several more quarters.

Admittedly, the administration has made some effort to tackle inflation: Early last spring, Carter cut $5 billion from his tax reduction bill as an anti-inflation gesture, and recently he proposed a $5 billion cut in fiscal 1979 spending. Moreover, policy makers say he is serious about making sizable budget cuts for fiscal 1980.

But the rest of the administration's anti-inflation efforts have been less promising. Carter's bid to get businesses and unions to reduce their 1978 wage-price demands from their 1976-77 average has run into a wall of opposition from organized labor, and efforts to cut costs stemming from government regulation have encountered stiff fights from other agencies.

Moreover, as was the case in 1977. Carter so far has stunned most opportunities to propose measures that might help dampen inflation, such as a rollback of next year's scheduled Social Security tax increase, or a delay in the 1979 boost in the minimum wage. He also allowed another costly farm bill to become law. And he has rejected using tax incentives to encourage wage-price moderation.

Prodded in part by the dollar crisis, the administration now has a subcabinet task force preparing a voluntary wage-price guidelines program, but here, too, skeptics are doubtful it can be effective. Most likely, policy makers ultimately will have to try to ride out the inflation surge - hoping that slowed growth next year will dampen wages and prices some.

The dollar situation is even more ephemeral, in many ways. Despite last month's explosion in the trade deficit, the nation's trade position is expected to improve somewhat in 1979, easing pressure on the dollar. And the Fed and Treasury, working jointly, have taken some steps to help stem the current dollar slide.

However, two of the other major factors in the dollar's slump - inflation and the lack of a serious energy program - are likely to continue. International analysts still believe generally that the dollar will stage a moderate comeback next year against the West German mark and most European currencies. As for the Japanese yen, however, as one analysts shrugs: "Anything can happen."

The outlook for the economy in 1979 points to two conflicting, and obviously painful, prospects - continued high inflation, and a slowdown in the economy, with a possible recession. Although prognosticators still want to see another quarter's statistics before nailing down their forecasts, the predictions generally fall into these ranges:

The underlying inflation rate - now at a painful 7 percent or more rather than the 6 to 6.5 percent Carter had projected for this year - is expected to continue high, and possibly even speed up further in 1979. Some economists even are predicting a rate of 8 percent or more in the next 15 months. (The temporary double-digit pace of early 1978 already is slowing.)

The economy's growth rate will slow further in 1979, possibly to between 2 and 3 percent for the year - a level that may or may not send the jobless rate rising again, depending on what happens to productivity. Importantly, a few analysts still are forecasting a brief - though hopefully moderate - recession, though most don't see the possibility until some time in 1980 at the earliest.

The growth rate for the current year is expected to end up at about 4 percent, just below the revised target the administration set last May. (Last January, Carter predicted the economy would grow by a more robust 4.7 percent this year and 4.8 percent in 1979. But he trimmed the 1978 forecast after the coal strike and bad weather last winter crimped policy makers' plans.)

The nation's unemployment rate, now 5.9 percent of the work force, is expected to continue at about that level for most of next year, assuming the economy doesn't plunge into a recession. But the fact that the jobless rate already is so close to what economists regard as "full employment" means there's unlikely to be much further improvement.

One element of relief in the updated forecasts is that chances of a recession in 1979 - regarded only a few months ago as a growing certainty - appear to have ebbed somewhat. One factor almost certainly is that the Fed's continued boost in interest rates hasn't crimped the economy as some analysts had figured - in part because of new regulations that safeguard housing funds.

Another simply is that, except for the worsened inflation outlook, few real storm clouds have appeared so far this year. Before the 1974 recession, for example, rapidly burgeoning inventories kept economists fretting. But this time, says Alan Greenspan, former President Ford's economic adviser, "There are no compelling imbalances that must be righted."

Indeed, forecasters seem to agree generally that the economy will move along next year largely on 1978's momentum. Recent figures have shown some weakening already in many many key sectors of the economy, from consumer spending to new factory orders. And there's little sign that the hoped for boomlet in needed business investment is apt to appear in 1979.

"The really big problem in policy is what to do about inflation," says Otto Eckstein, head of Data Resources Inc. With the present wage-price program done in, Carter now must turn inevitably to some form of guidelines. "But the labor movement has gone out of its way to expose Carter's weak point," Eckstein says. "To have numerical guideposts would be compounding the problem."

The outlook includes these forecasts for key U.S. industries:

Home building. Starts will decline in 1979 to around 1.7 million from a more robust 1.9 million in 1978 - respectable, but not nearly as stimulative in overall economic terms. Moreover, if interest rates rise very substantially from the present levels, it could crimp production even further.

Capital goods. Nonresidential construction and production of heavy equipment and machinery will rise moderately in 1979 - by between 4 and 4.5 percent, according to most forecasts - enough to ward off any real recession, but not vigorously enough to spur the economy more rapidly.

Autos. This volatile American industry, whose performance affects one out of every 10 jobs in the economy, is expected to weaken some in 1979, with sales totaling just over 10 million compared with more than 11 million in 1978. But performance still will be respectable, with trucks taking up some of the slack.

Steel. Though there's substantial dependence on the auto industry, steel makers still expect a good sales year, about in line with 1978's performance, but still far from traditional recession levels. A good deal could depend on pricing and competition from abroad.

What Carter will do to cope with these problems remains to be seen. Under a new, stepped-up deadline, the subcabinet task force on inflation is scheduled to submit recommendations to the White House next week for a new, tougher anti-inflation program that includes voluntary wage-price standards to be "enforced" by government actions designed to pressure would-be violators.

And Carter is expected to be tougher than usual in holding down spending in the fiscal 1980 budget due out next January. Planning for the January spending plan already is well under way, and expectations are that the administration will try to pare the budget deficit sharply enough to guarantee visible cutbacks in some key areas.