
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
On the $8 \times 8$ chessboard, pieces are placed according to the following rule. Initially, the board is empty. A move consists of placing a piece on any empty square. With this move, exactly one of the pieces that end up on an adjacent square is removed from the board (if such an adjacent piece exists). What is the maximum number of pieces that can be placed on the board, considering the given rule? Adjacent squares are those closest by horizontal, vertical, or diagonal proximity.

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