
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
Suppose a larger cube composed of $64$ smaller identical cubes is arranged in a $4 \times 4 \times 4$ formation. Each face of the large cube has a distinct shading pattern that is mirrored exactly on its opposite face. Only the central $2 \times 2$ area of each face and one corner cube are shaded. Determine the total number of smaller cubes that must have at least one face shaded.
A) 14
B) 16
C) 18
D) 20
E) 22

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