
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
Given integers \( m \) and \( n \) such that \( m, n \in \{1, 2, \cdots, 1981\} \) and

\[
\left(n^{2} - m n - m^{2}\right)^{2} = 1,
\]

find the maximum value of \( m^{2} + n^{2} \).

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