
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
A regular dodecahedron is constructed using twelve congruent regular pentagonal faces, each of a different color. How many distinguishable ways are there to color the dodecahedron? (Two colored dodecahedrons are distinguishable if neither can be rotated to look just like the other.)

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