
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
Determine the number of different painting schemes for a triangular prism ABC-DEF, where each vertex is painted with one color and the two endpoints of each edge are painted with different colors, with five different colors available.

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