
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
Initially, there is a rook on each square of a chessboard. Each move, you can remove a rook from the board which attacks an odd number of rooks. What is the maximum number of rooks that can be removed? (Rooks attack each other if they are in the same row or column and there are no other rooks between them.)

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