
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 pairs of positive integers  $ m$  and  $ n$  that satisfy (both) following conditions:

(i)  $ m^{2}\minus{}n$  divides  $ m\plus{}n^{2}$  

(ii)  $ n^{2}\minus{}m$  divides  $ n\plus{}m^{2}$ 

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