
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
What is the maximum number of colors needed to paint all the cells of a 4 by 4 square so that for each pair of different colors, there exist two cells of these colors located either in the same row or in the same column of the square?

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