
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
The integer \(m\) is a perfect cube exactly when it is equal to \(n^{3}\) for some integer \(n\). Let \(m = 2^{4} \times 3^{2} \times 5^{5} \times k\). Determine the smallest positive integer \(k\) for which \(m\) is a perfect cube.

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