
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
Each of the 12 edges of a cube is labeled '0' or '1'. Two labelings are considered different even if one can be obtained from the other by any number of rotations and/or reflections. Determine the number of labelings such that the sum of the labels on the edges of each of the 6 faces of the cube equals 3.
A) 4
B) 6
C) 8
D) 10
E) 12

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