
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
Calculate the number of different ways to color the faces of a regular pentagonal pyramid with 5 different colors, where each of the five lateral faces is labeled with numbers 1, 2, 3, 4, and 5, and no two adjacent faces (sharing a common edge) can be the same color.

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