
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 $4 \times 4 \times 4$ cube is composed of $64$ identical smaller cubes. If one face and its opposite are shaded such that the 4 corner cubes and 4 center cubes in a square arrangement (2x2) are shaded, calculate the total number of smaller cubes that are shaded on at least one face.

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