
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
The ellipse \(\frac{x^{2}}{m^{2}}+\frac{y^{2}}{n^{2}}=1\) (\(m, n > 0\)) passes through the fixed point \(P(a, b)\) (where \(a, b\) are given real numbers, and \(a b \neq 0\), \(|a| \neq |b|\)). Find the minimum value of \(m+n\).

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