
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
Solve the equation  $m^{gcd(m,n)} = n^{lcm(m,n)}$  in positive integers, where gcd( $m, n$ ) – greatest common
divisor of  $m,n$ , and lcm( $m, n$ ) – least common multiple of  $m,n$ .

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