
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 nine squares of a $3 \times 3$ board must be painted in such a way that in each column, each row, and each of the two diagonals, no two squares have the same color. What is the minimum number of colors required to achieve this?
(a) 3
(b) 4
(c) 5
(d) 6
(e) 7

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