
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
We have a cube with an edge length expressed in centimeters as a whole number. All of its faces are painted red, and then we cut it into smaller cubes with an edge of $1 \mathrm{~cm}$.

- Lukáš claims that the number of smaller cubes with two painted faces is ten times the number of those with three painted faces.
- Martina says that the number of smaller cubes with two painted faces is fifteen times the number of those with three painted faces.

Only one of them is correct — who? And what was the edge length of the original cube?

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