
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
Consider all possible partitions of an 8 by 8 chessboard into dominoes, each consisting of two adjacent cells. Determine the maximum natural number \( n \) such that for any partition of the 8 by 8 board into dominoes, one can find a certain rectangle composed of \( n \) cells of the board that does not contain any whole domino. The side lengths of the rectangle in cells can be any natural numbers starting from one.

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