$2.$ The figure below shows a chess game that has progressed near the end. Using the minimax algorithm, predict how the game will progress.

a$.$ Draw a minimax search tree to depict how the game will progress. The search tree does not have to be complete, i$.$e$.$ does not have to include all possible branches. However, your answer must satisfy the following requirements:

i$.$ The start of the search tree is the current game state and the current player is White. Let white be MAX.

ii$.$ Use upward pointing triangle for MAX nodes $($maximization operations$)$ and downward pointing triangle for MIN node $($minimization operations$).$ Use square$/$rectangular box to represent terminal nodes.

iii. The search tree must include $($you can omit other branches$)$:

iv$.1$ branch where White wins $($checkmate$)$ in $1$ step.

v$.1$ branch where White wins $($checkmate$)$ in more than $1$ step.

vi$.1$ branch where Black wins $($checkmate$).$

vii. Indicate the utility value $($minimax value$)$ in every node $($MAX$,$ MIN and terminal$)$ in the search tree. Utility value must be written inside each node.

viii. The utility value when White wins is $100,$ when Black wins is $-100.$ The utility value is penalized by $-1$ for each step when being back propagated.

ix$.$ The actions should be labeled on each link $($edge$)$ following this convention: $[$color$][$piece$]-[$board location$].$ Example: Black king move to b$8$: BK$-$b$8.$

Color $/$ Piece Letter

White Color W

Black Color B

King Piece K

Queen Piece Q

b$.$ Based on the above search tree, state which action will the White take. State the reason. Note these three branches are part of a larger search tree if you explore all possible actions $($may lead to deeper branches$).$ Heuristics may be used for deep branches. The decision will be similarly guided by the minimax values as demonstrated in this question.