
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
Label each vertex of a cube with an integer from 1 to 8 (each integer used exactly once) such that the sum of the four numbers on each face of the cube is the same, and determine the number of distinct ways this can be done, considering rotations of the cube that make the labeling overlap as the same.

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