
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 baker creates a large birthday cake in the shape of a $5 \times 5 \times 5$ inch cube. The cake has icing on the top, the front face, and the left face, with no icing on the bottom, right, and back faces. The cake is uniformly cut into $125$ smaller cubes, each measuring $1 \times 1 \times 1$ inch. Determine how many of these small pieces will have icing on exactly two sides.
A) 29
B) 30
C) 31
D) 32
E) 33

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