
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 complex numbers \( z_{1}, z_{2}, z_{3} \) that satisfy:
\[ \left|z_{1}\right| = \left|z_{2}\right| = \sqrt{3}\left|z_{3}\right|, \quad z_{1} + z_{3} = z_{2} \]
Find the value of \( \frac{z_{1} z_{2}}{z_{3}} \).

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