
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
Given that each face of a regular tetrahedron is painted one of four colors such that two colorings are indistinguishable if two congruent tetrahedra with those colorings can be rotated to appear identical, determine the number of distinguishable colorings possible.

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