
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 $a, b, c, d, e$ be real numbers. Suppose that all the roots of $z^5 + az^4 + bz^3 + cz^2 + dz + e = 0$ are complex numbers lying on a circle in the complex plane centered at $0+0i$ and having radius $2$. The sum of the reciprocals of the roots is necessarily:
A) $-\frac{a}{4}$
B) $\frac{a}{4}$
C) $-\frac{a}{2}$
D) $\frac{a}{2}$

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