
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 such triple natural numbers \( m, n, \) and \( l \) that satisfy the following conditions:
\[ 
m + n = (\gcd(m, n))^2, \\
m + l = (\gcd(m, l))^2, \\
n + l = (\gcd(n, l))^2.
\]

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