
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
What is the maximum number of white and black pawns that can be placed on a $9 \times 9$ checkerboard (a pawn, regardless of its color, can be placed on any square of the board) so that none of them can capture any other (including those of the same color)? A white pawn captures two adjacent squares on the diagonals on the next higher row, and a black pawn captures two adjacent squares on the diagonals on the next lower row.

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