
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 cheesecake is shaped like a $3 \times 3 \times 3$ cube and is decorated such that only the top and three of the vertical faces are covered with icing. The cake is cut into $27$ smaller cubes, each $1 \times 1 \times 1$ inch. Calculate the number of the smaller cubes that will have icing on exactly two sides.

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