
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 large cube is composed of $64$ smaller identical cubes arranged in a 4x4x4 format. Each face of the large cube has a pattern where the diagonal from one corner to its opposite corner is shaded. For each face of the large cube, the opposite face is shaded in the same way. Determine the total number of smaller cubes that must have at least one face shaded.
A) 24
B) 28
C) 32
D) 36
E) 40

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