
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
Find all positive integers  $k$  for which the equation:   $$  \text{lcm}(m,n)-\text{gcd}(m,n)=k(m-n) $$   has no solution in integers positive  $(m,n)$  with  $m\neq n$ .


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