
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 \( z_1 \) and \( z_2 \) that satisfy \(\left|z_1\right| = \left|z_1 - 2 z_2\right|\) and \( z_1 \overline{z_2} = \sqrt{3}(1 - \mathrm{i}) \), where \(\mathrm{i}\) is the imaginary unit, find \(\frac{z_1}{z_2}\).

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