For the first time in the history of the American republic, one of our own is in the Oval Office. His day job may have been running a property empire but, as a successful reality star who still retains an executive producer credit, the 45th President of the United States is unquestionably a TV guy.

That experience gives Donald Trump an “attack is the best form of defence” confidence in his handling of the media. He banned from his campaign those publications that he claimed were reporting on him unfairly.

Since his inauguration, he’s attempted to set up a classic showbiz system of incentives to influence press coverage, rewarding “good behaviour” with preferential access, while sending those journalists he deems to be hostile to Coventry.

An assiduous spreader of false and fantastical claims himself, he has taken to using the term “fake news” to delegitimise any media reports that don’t suit him.

He is bolder and more adept than any previous Western politician in using Twitter and other digital platforms to get his message out directly to the public and over the heads of the media. Even this seems to be built on lessons in viral marketing learned in modern reality TV.

So how should the media respond? First, by not falling into the trap of becoming a political opposition: our responsibility is to report his presidency rigorously, but also objectively and fairly.

Second, by confronting the new President’s unprecedented willingness to bend or break the truth by rethinking some of our own traditional editorial boundaries.

The New York Times has now twice used the word “lie” to describe public statements by Trump, because that’s what they were.

Fact-checking used to be an activity consigned to paragraph nine, or put in a box at the bottom of the story. Now we routinely add words “falsely” or “with no evidence” to headlines about new remarks by Trump, as in “Trump claims, with no evidence, that ‘millions of people’ voted illegally”.

We need to stand up for our independence corporately, as well. Soon after the election, Trump summoned the leadership of American TV journalism to Trump Tower for an off-the-record dressing-down – one unnamed executive described it as a “fucking firing squad”.

The President-elect was due to pay a visit to the New York Times the very next day, but a critical difference was that our Chairman and Publisher, Arthur Sulzberger, had insisted that the main meeting at the Times should be an on-the-record meeting with our editors and journalists.

Mr Trump began the day by tweeting that he wouldn’t be coming after all – falsely claiming that we had changed the terms of the visit. In the end, he did turn up and spent an hour and a quarter answering our questions.

A day that began with him describing us as the “failing @nytimes” ended with him telling the rest of the world’s media, gathered in our lobby downstairs, that the Times was a “jewel” for America and the world. Go figure.

He has subsequently reversed or contradicted many of the answers he gave us that day – about torture, immigration and much else.

I asked him, given his pledge during the campaign to tighten America’s libel laws, whether he supported the First Amendment, which guarantees the freedom of the press. He replied: “I don’t think you’ll have anything to worry about.”

Is that a commitment he will keep? One of the reasons that audiences around the world took to reality formats such as The Apprentice was their unpredictability – you never knew just what was going to happen next. Now, one of the most idiosyncratic and protean stars of reality TV is installed in the White House. It’s going to be a white-knuckle ride.

Mark Thompson is President and CEO of the New York Times.