
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 that the non-zero complex numbers \( z_{1}, z_{2}, z_{3} \) satisfy \( z_{1} + z_{2} + z_{3} = 0 \) and \( |z_{1}| = |z_{2}| = |z_{3}| \), determine the shape of the triangle formed by the points \( Z_{1}, Z_{2}, Z_{3} \) corresponding to the complex numbers \( z_{1}, z_{2}, z_{3} \).

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