
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
A grid of $n \times n$ composed of small squares with a side length of 1 is colored with either white or black. The requirement is that for any rectangle, the four corners of the small squares are not all the same color. Determine the maximum value of the positive integer $n$.

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