
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 nut has the shape of a regular hexagonal prism. Each lateral face of the nut is painted in one of three colors: white, red, or blue, with adjacent faces painted in different colors. How many different nut paintings are possible? (It is not necessary to use all three colors in the painting.)

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