
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 \( x^2 - nx + 3 = 0 \). Suppose that \( c + \frac{2}{d} \) and \( d + \frac{2}{c} \) 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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