
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
Consider a central pentagon colored red. Around this central pentagon, five triangles are placed, each sharing one side with the pentagon. Each triangle or the pentagon must be colored either red, yellow, or green in such a way that no two adjacent polygons have the same color. In how many different ways can the pentagon and surrounding triangles be colored, given that the central pentagon is already colored red?

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