
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 \(200 \times 200\) chessboard, some cells contain either a red or a blue piece, while the other cells are empty. If two pieces are in the same row or column, one piece is said to "see" the other piece. Suppose each piece can see exactly five pieces of the opposite color (and 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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