Consider Grover's algorithm for the case $n=3.$

$($a$)$ Assuming that function $f$ satisfies $f(000)=f(001)=f(010)=f(011)=f(100)=f(101)=0,f(110)=f(111)=1,$ find the state after passing F gate.

$($b$)$ Find the status after passing through the assessment gate once.