
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 include the reciprocals of the three roots of $f(x)=x^4 + ax^3 + bx^2 + cx + d$. Additionally, $g(x)$ has a root at $x = 0$. Given $1 < a < b < c < d$, compute $g(1)$ in terms of $a, b, c,$ and $d$.
**A)** $\frac{1 + a + b + c}{d}$  
**B)** $\frac{a + b + c + d}{d}$  
**C)** $\frac{1 + a + b + c + d}{d}$  
**D)** $\frac{1}{d}$  
**E)** $\frac{b + c + d}{a}$

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