
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
Consider a $12 \times 12 \times 12$ cube, which is constructed from sixty-four $3 \times 3 \times 3$ smaller cubes. In a new design, we remove the centre cube from each face of the large cube and two centre cubes along one axis within the cube completely. Each of the fifty-six remaining $3 \times 3 \times 3$ cubes is then modified by removing one corner cube and the three cubes adjacent to it on each face. Calculate the surface area of the resulting structure.
A) 3276 square units
B) 3408 square units
C) 3552 square units
D) 3696 square units

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