
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
How many integers $n \geq 2$ are there such that whenever $z_1, z_2, ..., z_n$ are complex numbers satisfying
\[|z_1| = |z_2| = ... = |z_n| = 1 \text{    and    } z_1^2 + z_2^2 + ... + z_n^2 = 0,\]
the numbers $z_1, z_2, ..., z_n$ are equally spaced on the unit circle in the complex plane?
**A)** 1  
**B)** 2  
**C)** 3  
**D)** 4  
**E)** 5

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