
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
Determine all pairs  $ (m,n)$  of natural numbers for which  $ m^2\equal{}nk\plus{}2$  where  $ k\equal{}\overline{n1}$ .

EDIT. <span style="color:#FF0000">It has been discovered the correct statement is with  $ k\equal{}\overline{1n}$ .</span>

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