
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 had a cube with an edge length in centimeters represented by an integer greater than 2. All its faces were painted yellow, and then we cut it completely into smaller cubes with edge length $1 \mathrm{~cm}$. These small cubes were sorted into four piles. The first pile contained cubes with one yellow face, the second with two yellow faces, the third with three yellow faces, and the fourth pile contained cubes with no yellow face. Determine the edge length of the original cube, given that at least one of the following statements is true:

- The number of cubes in the first and fourth piles are in the ratio $4:9$.
- There were three times as many cubes in the first pile as in the second pile.

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