
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 nonzero complex numbers \( z \) have the property that \( 0, z, \) and \( z^2, \) when represented by points in the complex plane, are the three distinct vertices of an equilateral triangle?
- A) 0
- B) 2
- C) 4
- D) 6

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