
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
Given the set \( A = \{ z \mid z^{2n-1} = \bar{z}, z \in \mathbf{C}, n \in \mathbf{N}, n \geqslant 2 \} \), how many right-angled triangles can be formed with vertices corresponding to the complex numbers in \( A \) in the complex plane?

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