The five men and six women who met in Philadelphia last month were given blank index cards and asked to write answers to two questions.

What would be a good thing to happen to the United States? And who could bring it about?

The United States could have "peace with all its enemies," one of them wrote in response to the first question.

And who could do that? "An extremely good president, Congress and Senate and a miracle from God."

The participants didn't know it, but their answers to these and other questions about President Reagan and U.S.-Soviet relations were part of an intense drive by the White House to prepare for next month's summit with Soviet leader Mikhail Gorbachev.

A speech that Reagan is planning to deliver in Denver on Tuesday is a direct outgrowth of what the Philadelphians had to say about the Strategic Defense Initiative, Reagan's proposed space-based missile defense system.

The two-hour discussion was scrutinized later by high-ranking assistants to Reagan and by Richard Wirthlin, the president's longtime pollster, whose firm set up two such sessions, known as "focus groups," last Oct. 5 in anticipation of the Reagan-Gorbachev summit.

The Philadelphia groups talked about their impressions of Reagan and Gorbachev, about their hopes and expectations for a summit meeting, and they responded to suggested themes and arguments about a treaty that Reagan and Gorbachev are expected to sign to eliminate medium- and shorter-range nuclear missiles from Europe.

The focus groups -- a common tool in commercial marketing strategy and, increasingly, in political campaigns -- are also having an impact on the biggest diplomatic ceremony of Reagan's presidency. While not influencing the substance of the superpower diplomacy, the technique is a key element of the strategy of selling the outcome to the American people, which is the next step of summit diplomacy.

Although it was not disclosed at the time, the White House used similar groups before Reagan's meetings with Gorbachev in Geneva and Reykjavik, and before his State of the Union speeches. In this case, the participants were recruited in Philadelphia by Wirthlin's firm to reflect a cross-section of the population, but they were not told in advance the purpose of the sessions. They met after work in a specially outfitted room where Wirthlin's analysts could watch and listen to their reactions without being seen.

The president is given a summary of the focus group discussions. Wirthlin said it gives Reagan "an opportunity to listen to the voice of the average American and provides him a way to understand the hopes and aspirations" of the public "without anyone intervening between him and the public."

Democratic pollster Peter Hart said that while a small focus group "doesn't make a world," it can add a valuable dimension beyond public opinion surveys. "The advantage of focus groups is that you can get people talking in their own words and language about problems," he said. "You can get underneath the numbers of a poll. You can get them to use words and phrases that you just can't get out of an interview. You get a depth and a feel."

The words and phrases used in Philadelphia will be echoed by Reagan in the weeks ahead.

This summit is different from Reagan's previous meetings with Gorbachev because it is the first to center on the expected signing of a major arms control agreement. The White House staff is using the focus group comments to help structure a campaign for Senate ratification of the intermediate nuclear forces (INF) treaty.

According to many public opinion polls, the INF agreement generally enjoys wide support among Americans. But the Philadelphia focus groups demonstrated to White House strategists that many people remain ignorant of the details of the treaty and that Reagan has plenty of room to influence their impressions of it.

"We have an opportunity to develop the landscape, the playing field," said Thomas C. Griscom, the White House communications director, who is taking a leading role in the summit planning along with Lt. Gen. Colin L. Powell, whom the president has named as his new national security adviser. They head a White House team trying to nail down the summit script, despite problems such as Friday's collapse of plans for Gorbachev to address Congress.

One of the surprising findings from the Philadelphia focus groups was that the participants saw little direct benefit from an arms agreement that wipes out midrange nuclear missiles in Europe. Rather, they attached more significance to the treaty as a "first step" toward reducing the big intercontinental nuclear missiles with which each superpower could attack the other.

This view of the treaty was evident when the focus groups were asked which themes they felt were most compelling for the summit. The highest score went to "First Step for Peace," which, according to the participants, was the most literal representation of how they felt. By contrast, the participants were ambivalent about "A Step in a New Direction." They were cool toward the theme, "Little More Hope for the Human Heart."

The White House subsequently adopted the "first step" idea as the theme of the summit. In a symbolic twist to show that the treaty is not the culmination of the summit, but rather a starting point, the document is to be signed on the second day of Gorbachev's meetings, rather than at the end, White House officials said.

The focus groups are just one part of the summit planning effort. In drawing up a five-page summit plan, Griscom also held talks with former Nixon administration aides who had dealt with Leonid Brezhnev's visit to the United States in 1973 and former Carter aides who engaged in the failed effort to ratify the 1979 SALT II treaty. Other White House officials are mapping legislative strategy, writing Reagan speeches, and recruiting outsiders to speak up for the INF treaty after the summit.

Another surprising finding of the focus groups was that most people have only a general concept of Reagan's missile defense system, commonly known as "Star Wars," which is now in the research phase. Reagan launched the program in 1983, saying he wanted to make nuclear missiles obsolete, and for several years the Soviets tried to block it. More recently, the Soviets have called for restrictions on its deployment.

The Philadelphia groups expressed ignorance about what role the missile defense system has played in the negotiations. Some of them expressed concern that SDI would be an offensive weapon, as opposed to Reagan's contention that it is strictly defensive. Wirthlin and his analysts concluded that Reagan should attempt to link the missile defense program to the strongly held notion that the Soviets cannot be trusted, and that SDI is an "insurance policy" against Soviet cheating.

White House officials said Reagan intends to highlight this point this week when he visits a Martin Marietta Corp. facility near Denver that is working on Star Wars technology. For visual impact, Reagan will be given a briefing on the "Zenith Star" project, a study that is part of the missile defense effort, and then speak to company workers.

Despite the recent improvement in U.S.-Soviet relations, the Philadelphia groups voiced a deep and continuing distrust of the Soviets, particularly on whether they would abide by a treaty.

Reagan has stated repeatedly that he would not settle for anything but the "most stringent" verification measures "in the history of arms control negotiations." But the focus group results suggested that many Americans remain uneasy about whether compliance can be verified. A senior White House official said verification is to be one of the major themes running through Reagan's push for Senate approval of the treaty.

Another surprising finding of the focus groups was the way people viewed the "peace through strength" theme that helped propel Reagan to the presidency. Reagan used the slogan in his 1980 campaign and in the early years of his first term to advocate the defense buildup. The focus groups said they liked the slogan as a way to describe the U.S. approach to the Soviets. But they expressed caution about using it as a theme for the summit on grounds that it wouldn't be appropriate as a "peace banner."

The Philadelphians were also asked their reaction to some of the recent criticisms of the INF treaty.

The criticism they found most compelling was that the United States could never be certain that all the nuclear missiles had been eliminated by the Soviets. They also gave weight to the argument that once the missiles were eliminated, the Soviets would have an advantage in conventional military arms in Europe.

These concerns have also found their way into Reagan's recent speeches. For example, on Oct. 28 at West Point, the president declared that the United States "will retain a large force of many types" in Europe and that further nuclear arms cuts can happen only with "substantial improvement" in the balance of conventional and chemical weapons.

Of less concern to the Philadelphians were arguments that the treaty would signal that the United States is abandoning its support for NATO and the European allies. The focus groups also did not attach much weight to criticism that the treaty eliminates only 4 percent of the existing nuclear warheads.

Wirthlin and others have long reported that Americans are of two minds toward the Soviets -- they want their leaders to be wary of them, but they also want to keep talking to them.

The Philadelphians seemed to bear this out. They said repeatedly that the Soviets cannot be trusted, but they still seemed to welcome a summit. At the opening of the sessions, more than half of the participants volunteered that "world peace" would be the best thing that could happen to the United States and, when asked about this, expressed the view that a summit would be a "significant event." By contrast, fewer than a fifth of the participants chose economic objectives -- a balanced budget, or full employment -- as a good thing that could happen to the nation.