Andres Manuel Lopez Obrador won over Mexican voters by promising a different kind of presidency, making sometimes theatrical pledges that many wondered how he would fulfil.

Less than a week into his presidency, he's holding daily news conferences to report on the status of his agenda, making updates that some Mexicans find hopeful and others worrying. His daily briefings mark a radical change from the previous, more tight-lipped Administration.

Since he took office on Sunday, some of his most unusual ideas have already been enacted. The former presidential mansion is now open to the public (and the new Alfonso Cuaron film will soon be projected on its walls). The presidential plane has been taken to California, where the Mexican Government will try to sell it in a show of austerity. Lopez Obrador is getting around in an old Volkswagen, rather than a glitzy motorcade.

Now, beyond the symbolic gestures, Lopez Obrador is preparing to tackle some of Mexico's biggest policy challenges. Next week, he said, he will announce a proposal to undo predecessor Enrique Pena Nieto's education overhaul, though he has released few details, aside from claiming that it was developed "with the consensus of teachers". In the coming days, Lopez Obrador said, he will speak to United States President Donald Trump about migration.

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On Tuesday, Lopez Obrador ordered a "truth commission" to investigate the disappearance of 43 students in Ayotzinapa in 2014. Security forces have been implicated in the incident, and Lopez Obrador's effort to shed light on what happened has given hope to some of the parents of the disappeared, even as it has raised questions about what a new investigation might yield.

On Wednesday, he struggled to convince investors that despite his recent attacks on neoliberalism - and particularly on Mexico's newly liberalised energy industry - he won't stand in the way of a free market. He pointed out on Tuesday, at his first news conference as President, that the markets had gone up during the first day of his term.

"You cannot regulate the market by decree," he said. "I am in favour of a free market."

Also on Wednesday, Lopez Obrador returned to his stated policy of capping the salaries of public officials, saying at a news conference, "It is dishonest when an official receives up to 600 thousand pesos a month [$42,400]. That is corruption."

Lopez Obrador seemed to recognise that some high-level officials are quietly seething at his proposal. Apparently addressing those who might be displeased, he said, "Then there is the private sector."

The newspaper El Universal reported on Wednesday that almost 3000 public employees have filed class-action lawsuits against the Government over a law mandating that no bureaucrat can earn more than the President. Because Lopez Obrador set his salary at 108 thousand pesos per month, less than half of his predecessor's salary, the pay of other public servants also has plummeted. According to El Universal, the penalty for government employees caught receiving a higher salary than the President is 14 years in prison.

On Tuesday, Lopez Obrador's nominee for foreign minister, Marcelo Ebrard, met with US Homeland Security Secretary Kirstjen Nielsen in Washington. They had been expected to discuss a plan that would force asylum seekers to remain in Mexico while their claims are processed in the US. But Ebrard called the meeting a "courtesy visit", and no deal was announced or alluded to.

On Thursday, at his daily news conference, Lopez Obrador said he would push for new oil drilling sites in the southern state of Campeche. "We need to extract oil. Production is falling. In a few days, we will start drilling new oil wells," he said.

But at the same news conference, he also put private companies that had received recent oil contracts on notice, saying he would be watching their performance closely before deciding whether to continue the contracts, injecting uncertainty into his energy policy, which has already unnerved many in the industry.

"From their results, we will make the decision. Our commitment is to give a period of three years for results," Lopez Obrador said.