
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
The large cube shown is made up of $64$ identical sized smaller cubes. Each face of the large cube has a distinct symmetric pattern with the opposite face shaded the same way. Specifically, in each pattern, the central $2 \times 2$ square and the four corner squares of each $4 \times 4$ face are shaded. Determine the total number of smaller cubes that must have at least one face shaded.
A) 18
B) 20
C) 22
D) 24
E) 26

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