
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
Place chess pieces on an $8 \times 8$ chessboard, with at most 1 piece per square, such that each row, each column, and each diagonal contains exactly an even number of pieces. What is the maximum number of pieces that can be placed on the board?

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