
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
Let \(a, b, c, d, m, n\) be positive integers such that \(a^{2}+b^{2}+c^{2}+d^{2}=1989\), \(a+b+c+d=m^{2}\), and the largest of \(a, b, c, d\) is \(n^{2}\). Determine, with proof, the values of \(m\) and \(n\).

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