
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 positive integers satisfying the conditions:
1. \( \gcd(m+n, 330) = 1 \),
2. \( m^m \) is a multiple of \( n^n \),
3. \( m \) is not a multiple of \( n \).
Find the least possible value of \( m+n \).

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