
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 a \(200 \times 200\) chessboard, some squares contain a red or blue piece, while other squares are empty. A piece is said to "see" another piece if both pieces are in the same row or column. Suppose each piece can see exactly five pieces of the opposite color (it may also see some pieces of the same color). Find the maximum total number of pieces on the chessboard.

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