
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
In how many different ways can the faces of a cube be painted using six given colors (each face must be painted entirely with one color), considering that only those colorings are different which cannot be made identical by rotating the cube?

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