
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
How many ways are there to arrange three indistinguishable rooks on a \(6 \times 6\) board such that no two rooks are attacking each other? (Two rooks are attacking each other if and only if they are in the same row or the same column.)

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