
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 the maximum value of  $m^{2}+n^{2}$ , where  $m$  and  $n$  are integers satisfying  $m,n\in \{1,2,...,1981\}$  and  $(n^{2}-mn-m^{2})^{2}=1.$ 

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