From left, Senate Majority Leader Mitch McConnell (R-Ky.), President Trump and House Speaker Paul D. Ryan (R-Wis.) during a meeting with House and Senate leadership at the White House in Washington on March 1. (Evan Vucci/Associated Press)

British politicians are familiar with the term “reshuffle,” when senior figures in the government switch portfolios or get tossed out or brought into the government. And they’re also very familiar with “coalition governments,” when ruling governments divide jobs and authorities between two or more parties. American politicians could find study of both concepts useful. The executive branch has completed a major reshuffle over the past month. If the White House can match that with a smart policy push, the coalition between the Trump White House and the Capitol Hill GOP, though battered, could come together again quickly out of shared self-interest.

I’ve been arguing for months that what we have in Washington is a coalition government between President Trump, his team and his core voters, and congressional Republicans led by Senate Majority Leader Mitch McConnell (Ky.) and House Speaker Paul D. Ryan (Wis.). The bridge between the coalition’s halves has often been kept open by the vice president, but the president himself has proven adept at quietly working with coalition’s many elements. Both the president and vice president can now spend some of the balance of the summer ensuring that it is indeed open and that there is traffic flowing in both directions.

As for the reshuffle, the exit of Stephen K. Bannon completes a restructuring of the West Wing that began almost as soon as the president took office and is now apparently complete. Like the physical renovation of the West Wing, it was noisy and not very attractive but necessary. The partnership between the executive- and legislative-branch Republicans simply could not have lasted without changes in the administration.

Six months in, the president has assembled the best national security team of my lifetime, led by Defense Secretary Jim Mattis. While his communications team remains somewhat in flux, interim communications director Hope Hicks has been at the president’s side since the beginning of his campaign and enjoys his confidence. Press secretary Sarah Huckabee Sanders is growing in confidence and command of the press briefing room. Vice President Pence’s new chief of staff , Nick Ayers, a capable staffer liked by all sides of the GOP, will be an invaluable resource not just to the vice president but to the president’s entire senior executive team.

On the domestic policy front, senior economic adviser Gary Cohn and White House Counsel Don McGahn, along with Jared Kushner and Ivanka Trump, are firmly in control of the domestic policy process. Committed reformers such as Attorney General Jeff Sessions, Environmental Protection Agency Administrator Scott Pruitt and Health and Human Services Secretary Tom Price are in strong and stable positions now as staffing of political appointees accelerates. (I leave out Rex Tillerson’s State Department, where there remains an extraordinarily high degree of instability.)

On the Hill, the congressional GOP is hungry for more success beyond the confirmation of Supreme Court Justice Neil M. Gorsuch. The Veterans Affairs reform bill and 14 Congressional Review Act laws , while enormously significant, were low-profile victories. The filling of dozens of additional federal court vacancies behind Gorsuch is getting organized and moving forward finally, and dozens of confirmations, particularly of the key circuit court openings, and perhaps the end of the anti-constitutional “blue slips” are crucial wins within reach too. But what is needed above all is either a tax bill or resurrection of a health-care fix. Slashing the corporate tax rate is probably the easiest (and perhaps most economically significant) bit of legislation to accomplish, but so too must arrive the repeal of the Budget Control Act, which has devastated national security via the “sequester” and hamstrung a key Trump promise — that of a 355-ship Navy. Both the corporate tax cut and repeal of the BCA are worth daring the Democrats to shutter the government over, as voters understand both are crucial to the well-being of the country.

A grand bipartisan agreement on infrastructure and immigration is within reach as well. Senators enjoying the president’s confidence such as Tom Cotton (R-Ark.) and David Perdue (R-Ga.) can team with reasonable senators across the aisle such as Christopher A. Coons (D-Del.) and Angus King (I-Maine) to draft a genuine breakthrough bill: one that delivers much-needed sanity to legal immigration goals, a legal form of Deferred Action for Childhood Arrivals and of course infrastructure funding, including a long, strong border fence — the visible expression of a genuine commitment to border security. Infrastructure funding — which is mostly block-granted to county governments — allows federalism’s beauty to work and puts Americans to work on needed projects quickly, and, if drafted the right way, won’t be as ineffective as 2009’s “stimulus.”

The last ingredient in a successful reset will be the president’s rhetoric. He gave great speeches in Saudi Arabia and Poland on crucial issues of Islamist extremism and the inherent goodness of the West. Now he needs to give some key addresses at home, about American equality and the essential demands of citizenship, including an iron commitment to the rule of law and respect for constitutional norms. He needs scribes who can help the president craft messages not in 140 characters but 40 or so minutes that raise the eyes of Americans to the wins for all Americans on the board and to shared goals of economic and national security for all Americans. There are already some talented writers in the Old Executive Office Building. Put them to work.

Trump’s strategic resolve must be to focus on a legislative agenda that does fit in 140 characters — a cut in the corporate tax rate, repeal of the defense sequester, a bigger Navy, a real border fence, a legal-immigration overhaul and originalist judges — combined with continued, reiterated strategic clarity toward the Islamic State, Iran, North Korea, Russia and China. If he works with his partners in Congress, these are all doable. And the team to help the president do it seems, finally, to be in place.