
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 cube is to be painted using six different colors, with each face of the cube painted a unique color. How many distinguishable ways are there to paint the cube? (Two colored cubes are distinguishable if neither can be rotated to look just like the other.)

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