
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 constructed using six congruent square faces, each of a different color. How many distinguishable ways are there to construct the cube? (Two colored cubes are distinguishable if one cannot be rotated to appear the same as the other.)

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