
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
In the cells of an $8 \times 8$ chessboard, there are 8 white and 8 black pieces arranged such that no two pieces are in the same cell. Additionally, no pieces of the same color are in the same row or column. For each white piece, the distance to the black piece in the same column is calculated. What is the maximum value that the sum of these distances can take? The distance between the pieces is considered to be the distance between the centers of the cells they occupy.

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