
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
From 6 different given colors, choose several colors to color the 6 faces of a cube. Each face must be colored with a different color, and adjacent faces must have different colors. How many distinct coloring schemes are there? (Two schemes that can be made to coincide through rolling and rotation of the cube are considered the same scheme.)

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