
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
Suppose \( m \) and \( n \) are positive integers for which:
- The sum of the first \( m \) multiples of \( n \) is 120, and
- The sum of the first \( m^{3} \) multiples of \( n^{3} \) is 4032000.

Determine the sum of the first \( m^{2} \) multiples of \( n^{2} \).

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