
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 the given six different colors, select several colors to paint the six faces of a cube, with each face painted exactly one color, and each pair of faces sharing an edge painted different colors. How many different coloring methods are there? (Note: If we can flip two identically painted cubes in such a way that the top, bottom, left, right, front, and back faces of the two cubes match in color, then we say the two coloring schemes are the same.)

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