
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
Consider a large cube that is made up of $27$ identical smaller cubes arranged in a $3 \times 3 \times 3$ formation. Each pair of opposite faces of the large cube is shaded such that one face has 4 cubes shaded (in each corner cube) and its opposite face has 3 cubes shaded forming a 'L' shape at one corner of the cube face. Calculate the total number of smaller cubes that have at least one face shaded.
A) 14
B) 16
C) 17
D) 19
E) 21

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