
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 constructed from $27$ smaller cubes of identical size. Each face of the large cube is shaded such that it matches its opposite face. Given that each face of the large cube has a different pattern from the original problem, with the top left, center, and bottom right smaller cubes shaded, determine the total number of smaller cubes that have at least one face shaded.
A) 10
B) 12
C) 15
D) 18
E) 21

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