
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
If \( z_{1}, z_{2}, z_{3} \) satisfy \( \left|z_{1}\right|=\left|z_{2}\right|=\left|z_{3}\right|=1 \), \( z_{1}+z_{2}+z_{3}=1 \), and \( z_{1} z_{2} z_{3}=1 \), then what is \(\left( z_{1}, z_{2}, z_{3} \right) \)?

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