
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 that the positive rational numbers \(a\) and \(b\) satisfy:
\[ a+b=a^{2}+b^{2}=s \]

If \(s\) is not an integer, then denote:
\[ s=\frac{m}{n} \text{ where } (m, n) \text{ are positive integers with } \gcd(m, n)=1. \]

Let \(p\) be the smallest prime factor of \(n\). Find the smallest possible value of \(p\).

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