
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 an \(8 \times 8\) chessboard, 6 black rooks and \(k\) white rooks are placed on different cells so that each rook only attacks rooks of the opposite color. Compute the maximum possible value of \(k\). (Two rooks attack each other if they are in the same row or column and no rooks are between them.)

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