We thought nothing could be more bizarre than Gladys Carrión stepping down as head of the city’s Administration for Children’s Services because it’s “best for my well-being.” But then we learned that Mayor Bill de Blasio made a big deal of promising to choose an independent monitor for ACS when he’d already been ordered to accept one.

It turns out the state Office of Children and Family Services’ investigation of the Zymere Perkins tragedy ended with a Dec. 1 mandate for ACS to appoint an independent monitor approved by OCFS.

The mayor in his public remarks specifically denied needing state approval for his monitor pick — a bald lie.

It looks like he didn’t keep Department of Investigation chief Mark Peters in the loop, either. Peters greeted word of the coming monitor by noting, “DOI is the independent monitor for ACS; we are not sure what another independent monitor would add.”

Then he got rough: “DOI has already released two independent reviews of ACS this year and will release a third, showing failures at the highest level, early next year. As DOI has informed City Hall, ACS needs leadership that will actually implement the recommendations that DOI and others have called for time and again.”

Those others include Public Advocate Letitia James, who’s been demanding a monitor for years — and who, after the death of 6-year-old Zymere in September, called ACS “fundamentally broken” and said Carrión had “failed to fix it.”

On Tuesday, James was restrained, saying, “I only wish it hadn’t taken litigation and crises involving more dead children to bring about this type of meaningful reform.”

Look: De Blasio made specific promises, back when he hired Carrión, to do better than his predecessors. Then he proceeded to ignore evidence of failure in damning reports not just from James, a fellow progressive, but also from Peters, his own hand-picked DOI chief.

Then, when the state finally said Enough!, the mayor tried to pass off the humiliation of an outside monitor as his own initiative.

We can understand why de Blasio would rather not admit his stunning managerial incompetence. But does he have to be a stunningly bad liar in trying to cover up his failures?