
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 $\bullet$  the sum of the first  $m$  multiples of  $n$  is  $120$ , and $\bullet$  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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