
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 $c$ and $d$ be the roots of the equation $x^2 - mx + 3 = 0$. Suppose that $c + \frac{1}{d}$ and $d + \frac{1}{c}$ are the roots of the equation $x^2 - rx + s = 0$. What is $s$?

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