
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


- $\gcd(m+n,210) = 1,$
- $m^m$  is a multiple of  $n^n,$  and
- $m$  is not a multiple of  $n$ .

Find the least possible value of  $m+n$ .

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