
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 size \( n \times n \) is composed of small squares with side length 1. Each small square is either colored white or black. The coloring must satisfy the condition that in any rectangle formed by these small squares, the four corner squares are not all the same color. What is the largest possible value of the positive integer \( n \)?

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