
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 has 12 edges, each labeled with a number 0 or 1. Two labelings are considered different even if one can be obtained from the other through rotations and/or reflections. Determine the number of labelings possible so that the sum of the labels on the edges of each of the 6 faces of the cube equals 3.

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