
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 with $0$ or $1$. Different labelings are considered distinct even if one can be obtained from the other by a sequence of rotations and/or reflections. Devise a method to label the cube such that the sum of the labels on the edges of each of the $6$ faces of the cube equals $2$, and additionally, all diagonally opposite edges must be labeled the same. How many such labelings are possible?
A) 2
B) 3 
C) 4
D) 5
E) 6

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