
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 larger cube is constructed from $64$ smaller cubes (forming a $4 \times 4 \times 4$ cube). For each face of the larger cube, only the border cubes along the edges of the face are shaded, and the opposite face is shaded in the exactly same pattern. Determine the total number of smaller cubes that must have at least one face shaded.
A) 55
B) 42
C) 36
D) 32
E) 28

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