
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
The plane is divided into unit squares. Each square is to be colored with one of \( n \) colors, so that the following applies: If four squares can be covered with an L-tetromino, then these squares have four different colors (the L-tetromino may be rotated and mirrored). Determine the smallest value of \( n \) for which this is possible.

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