
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 constructed from $64$ identical-sized smaller cubes in a 4x4x4 arrangement. Each face of the large cube, alongside its opposite face, has a unique shading pattern as follows: two diagonal lines from opposite vertices. Calculate the total number of smaller cubes that must have at least one face shaded.
A) 22
B) 24
C) 26
D) 28
E) 30

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