
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 5x5x5 inch cake, where each layer is composed of 1-inch cubes, is decorated with icing on the top, the front, and the right side faces, but not on the bottom, back, or left side faces. The entire cake is cut into 1x1x1 inch smaller cubes. How many of these 125 smaller cubes will have icing on exactly two faces?
A) 30
B) 32
C) 34
D) 36
E) 38

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