
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
Given an icosahedron, which is composed of 20 equilateral triangular faces, how many different colors are needed to color these 20 faces such that no two adjacent faces share the same color?

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