
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 \( g(x) \) be a polynomial with leading coefficient \( 1 \), whose roots are the reciprocals of the two roots of \( f(x) = x^2 + px + q \), where \( p < q \). Determine \( g(1) \) in terms of \( p \) and \( q \).
**A)** \( \frac{1+p}{q} \)  
**B)** \( \frac{1+q}{p} \)  
**C)** \( \frac{1+p+q}{q} \)  
**D)** \( 1+p+q \)  
**E)** \( \frac{q}{1+p+q} \)

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