Assume that the year is now $2023.$ President Bieber $($a Democrat, elected to office in $2022)$ disagrees with various positions taken on Food and Drug Administration $($FDA$)$ matters by FDA director S$.$ Gomez, who was appointed to her post in $2021$ by then$-$President Jolie $($a Republican$).$ President Bieber has therefore sent Gomez a letter stating that she is discharged as FDA director. Gomez, however, refuses to relinquish her position. Who is acting lawfully here?

Multiple Choice

Gomez, because she is removable only for cause, which does not exist here.

President Bieber, because the head of any administrative agency is removable at the President$$s will.

President Bieber, because of the type of agency FDA is$.$

Gomez, because the President does not have unlimited authority over independent agencies such as FDA.