Federal and state prosecutors will follow a delicate legal choreography after characterizing Mr. Mangione’s actions differently in the fatal shooting of Brian Thompson.

© Jefferson Siegel for The New York Times

Federal authorities filed a total of four counts against Luigi Mangione, who is accused of killing Brian Thompson, the chief executive of UnitedHealthcare.

© Alan Chin for The New York Times

The nature of the potential charges against Luigi Mangione was unclear, but they could allow federal prosecutors to seek the death penalty.

© Karsten Moran for The New York Times

The president can still do a lot before he leaves the White House.