$(10\%)$ Given a NDPA, $Q=\{q_0,q_1,q_1,q_2\},=\{a,b\},=\{0,z\},$ and $F=\{q_2\}$ with

$(q_0,a,z)=\{(q_0,0z)\},$

$(q_0,a,0)=\{(q_0,00)\},$

$(q_0,(b),0)=\{(q_1,)\},$

$(q_1,(b),0)=\{(q_1,)\},$

$(q_1,,z)=\{(q_2,z)\}.$

$($a$)$ Show that it accepts the string aaabbb.

$($b$)$ What language is accepted by the npda?