
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 triples  $m$ ;  $n$ ;  $l$  of natural numbers such that  $m + n = gcd(m; n)^2$ ;  $m + l = gcd(m; l)^2$ ;  $n + l = gcd(n; l)^2$ :
*S. Tokarev*

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