
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 four roots are the reciprocals of the four roots of \( f(x) = x^4 + ax^3 + bx^2 + cx + d \), where \( 1 < a < b < c < d \). Determine the value of \( g(1) \) in terms of \( a, b, c, \) and \( d \).
**A)** \( \frac{1 + a + b + c}{d^2} \)  
**B)** \( 1 + a + b + c + d \)  
**C)** \( \frac{1 + a + b + c + d}{d} \)  
**D)** \( \frac{a + b + c + d}{d^2} \)  
**E)** \( \frac{1 + a + b + c + d}{a + b + c + d} \)

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