
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 confectioner made a cake shaped like a $5 \times 5 \times 5$ inch cube for a special event. The cake has icing on the top face and all four lateral faces, but not on the bottom face. The cake is uniformly cut into $125$ smaller cubes, each measuring $1 \times 1 \times 1$ inch. Determine the number of $1 \times 1 \times 1$ inch cubes that have icing on exactly two sides.
**A)** 28
**B)** 30
**C)** 32
**D)** 34
**E)** 36

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