
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 cube of edge $5$ cm is split into multiple smaller cubes such that not all cubes have the same size. Each edge of the smaller cubes must also be a whole number of centimeters. Determine $N$, the number of smaller cubes resulting from this division.
A) 100
B) 117
C) 118
D) 125
E) 133

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