
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 $a, b, c, d$ be real numbers and $k$ be a non-zero real number. Suppose all roots of the polynomial $kz^4 + az^3 + bz^2 + cz + d = 0$ are complex numbers lying on a circle in the complex plane centered at $0 + 0i$ and having a radius $2$. What is the sum of the reciprocals of the roots?
A) $\frac{a}{4k}$  
B) $-\frac{a}{4k}$  
C) $\frac{b}{4k}$  
D) $-\frac{b}{4k}$

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