
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
In a $4 \times 4$ grid, cells are colored in various colors such that in any $1 \times 3$ rectangle, there are at least two cells of the same color. What is the maximum number of colors that can be used?

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