
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 \( z \) satisfy the condition that the points \( 0, z, \) and \( z^6 \) in the complex plane form the vertices of a right triangle with the right angle at \( z \)?
A) 0
B) 1
C) 3
D) 5
E) Infinitely many

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