
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
a) On each of the squares in the top and bottom rows of an $8 \times 8$ chessboard, there is a piece: white pieces on the bottom, black pieces on the top. In one move, it is allowed to move any piece to an adjacent free square either vertically or horizontally. What is the minimum number of moves required to have all the black pieces on the bottom and all the white pieces on the top?

b) The same question for a $7 \times 7$ board.

Present the answer in LaTex format: \boxed{Your answer}
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