
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
Let \( m \) and \( n \) be relatively prime positive integers. If \( m^{3} n^{5} \) has 209 positive divisors, then how many positive divisors does \( m^{5} n^{3} \) have?

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