Will Trump ever stop treating his presidency as a reality-TV show?

As Donald Trump careered through another eventful week in his presidency it was easy to forget the serious foreign-policy and economic issues that are in the hands of the world's most powerful leader.

As the controversy about the US president's potentially illegal payment to an adult-film star gripped Washington, a high-level delegation led by his treasury secretary, Steve Mnuchin, landed in Beijing for trade talks. They did not go well. Both sides hardened their positions: the United States demanded that China reduce its trade surplus with the US by $200 billion over two years; Beijing rejected the idea.

And trade tensions between the US and the European Union continue. Although the Trump administration last week granted Europe an extra 30 days' reprieve from aluminium and steel tariffs, the US commerce secretary, Wilbur Ross, said the move was only temporary. The EU shot back that it would not negotiate under threat.

Further challenges loom in foreign policy in what could be a critical few weeks for the Trump presidency. By the end of this week the president will decide whether to stay in the Iran nuclear deal, while details about the upcoming summit with the North Korean leader, Kim Jong-un, are expected in the coming days.

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As with many aspects of his life, Donald Trump treats big foreign-policy decisions as if they were part of a reality-TV show, keeping his audience in suspense before revealing the big climax. Take his tweet this week about a trio of Americans being detained by North Korea. "As everybody is aware, the past Administration has long been asking for three hostages to be released from a North Korean Labor camp, but to no avail. Stay tuned!" On Thursday morning Rudy Giuliani – the former mayor of New York who is now the president's newest lawyer on the special-counsel investigation, and who is not supposed to be party to national-security decisions – breezily told Fox News's morning chatshow that the hostages would be released by the end of the day. It didn't happen.

Similarly, Mr Trump has left the world wondering about his next moves on Iran, which agreed in 2015 to curb its nuclear programme in return for the lifting of international sanctions. During press conferences at the White House the leaders of France and Germany, which are two of the countries that cosigned the deal, were forced to concede after their one-on-one meetings that they did not know if the president would withdraw.

As Trump toys with the idea of pulling out of the Iran agreement and meeting his former foe Kim Jong-un, myriad issues present themselves. So far there is little indication of what the US wants from the meeting with the North Korean dictator. Although the failures of the North Korean agreements under the Clinton and George W Bush presidencies are still fresh in people's minds, the stakes are higher this time, as the president himself prepares to travel to meet Mr Kim.

Again, Trump's eye for theatrics is to the forefront of the decision-making process: he said last week that he wanted the summit to be held in the demilitarised zone between North and South Korea, as he liked the message it would send.

But a central paradox of the meeting is that the US president is boasting about his peace-building credentials with a nuclear power even as he mulls pulling out of the Iran deal, a deal that Germany, France and the UK have been trying to persuade him is the best way to stop Iran from developing nuclear weapons.

An expert in the art of deflection, Mr Trump knows the value  of a big foreign-policy decision to his presidency, providing a welcome distraction from troubles at home

The EU and other negotiators described the Iranian president, Hassan Rouhani, and foreign minister, Javad Zarif, as people they could work with, if not quite as the "moderates" they are sometimes termed. Officials from European capitals have reacted with frustration to the Trump administration's understanding of a deal that was, by its nature, flawed but served its main purpose of curbing Iran's nuclear activity.

The European signatories to the deal are set to present a separate political agreement to the White House this week that commits to taking a tougher stance on Iran, but it is unclear if this will be enough to keep the Americans on board. Iran has already warned that it will not renegotiate the deal; European capitals have begun to make plans to shield European companies in Iran if the United States reimposes sanctions.

An expert in the art of deflection, Mr Trump knows the value that a big foreign-policy decision can bestow on his presidency, providing a welcome distraction from troubles at home. As he tweeted last week: "There was no Collusion (it is a Hoax) and there is no Obstruction of Justice (that is a setup & trap). What there is is Negotiations going on with North Korea over Nuclear War, Negotiations going on with China over Trade Deficits, Negotiations on NAFTA, and much more. Witch Hunt!"

That the president can hold such diametrically opposed positions, threatening to withdraw from one nuclear deal while initiating another, is a measure of how much Trump’s decisions are based on what delivers the best headlines and resonates with his base, rather than on any considered thinking.

Trump may think that the possibility of bringing peace to North Korea – and even earning a Nobel Peace Prize, as suggested by the South Korean president, Moon Jae-in – may guarantee his place in history, whatever the finding of the Mueller investigation. But he would do well to remember the lessons learned by one of his predecessors. Richard Nixon may have made history when he visited China in 1972, but it was his impeachment, after the Watergate scandal, that defined his legacy. Trump may go to Korea, but in Washington the year-long investigation into Russian interference in the 2016 election will continue. Ultimately, impeachment could be the legacy of the 45th president of the United States.