
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
Suppose $a, b, c, d, e$ are real numbers. Consider the polynomial $z^5 + az^4 + bz^3 + cz^2 + dz + e = 0$ where all roots lie on a circle centered at the origin in the complex plane with radius 2. Determine the sum of the squares of the reciprocals of the roots.
A) 3
B) 4
C) 5
D) 6

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