
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 cake is shaped like a $5 \times 5 \times 5$ cube and has icing on the top, front, and right sides only. Determine how many of the small cubes have icing on exactly two sides.

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