
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 \(a\) and \(b\) be the roots of the equation \(x^2 - mx + 6 = 0\). Suppose that \(a + \frac{1}{b}\) and \(b + \frac{1}{a}\) are the roots of the equation \(x^2 - px + r = 0\). Find the value of \(r\).

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