
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
Tom Sawyer needs to paint a very long fence such that any two boards spaced exactly two, three, or five boards apart from one another must be painted different colors. What is the minimum number of colors Tom requires for this task?

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