
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 a chessboard, 32 white and 32 black pawns are placed in all squares. A pawn can capture pawns of the opposite color by moving diagonally by one square and occupying the position of the captured pawn (white pawns can capture only right-up and left-up, while black pawns can capture only left-down and right-down). Pawns cannot move in any other ways. What is the minimum number of pawns that can remain on the board?

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