
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 $12 \times 12 \times 12$ cube is composed entirely of $2 \times 2 \times 2$ smaller cubes. First, the center $2 \times 2 \times 2$ cube of each face, as well as the very center $2 \times 2 \times 2$ cube of the larger cube, are removed. Then, from the remaining cubes, any cube touching any face of the larger cube is further reduced by removing its cube that touches the outer face. Calculate the surface area of the final structure.
A) 3240  
B) 3304  
C) 3824  
D) 4032  
E) 4296

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