
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
Choose a number of colors from six different colors to dye the six faces of a cube, with each face dyed in a single color, ensuring that any two faces sharing an edge are dyed with different colors. Given that two coloring schemes are considered the same if one can be transformed into the other by rotating the cube, determine the total number of distinct coloring schemes.

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