
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 consists of $64$ smaller cubes (organized in an $4 \times 4 \times 4$ structure). Each face of the large cube has a specific shading pattern, and opposite faces are shaded identically. The pattern on one visible face is as follows: a $2 \times 2$ block at each of the four corners of the face is shaded. Determine the total number of smaller cubes that have at least one face shaded.
A) 36
B) 40
C) 44
D) 48
E) 52

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