a state diagram of an automaton with alphabet a$-($Z$,$ A$,$ B$,$ DELTA, LAMBDA$)$ is given. Define the given automaton using the quintuple $($Z$,$ A$,$ B$,$ DELTA, LAMBDA$).$ b$-$Assume that when the input sequence aaabbaa starts, the automaton A is in state z$2.$ Determine the final state and output sequence. c$-$Find all input sequences that lead from state z$2$ to state z$3."$