
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
Let \( z_{1} \) and \( z_{2} \) be a pair of conjugate complex numbers. If \(\left|z_{1} - z_{2}\right| = \sqrt{6}\) and \(\frac{z_{1}}{z_{2}^{2}}\) is a real number, then find \(\left|z_{1}\right|\).

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