$(5$ pts$)$ What is a steepest hill$-$climbing search? List two variations of the hill$-$climbing

search that can improve its efficiency.

$(5$ pts$)$ Define the evaluation function for $A^{**}$ search. Explain the conditions that will make

$A^{**}$ to be optimal.

$(5$ pts$)$ Explain validity and satisfiability in the context of logical agent and give an example

of each.