
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 complex numbers ${z_1}=2i$, ${z_2}=1-i$, where $i$ is the imaginary unit,

(1) Find the conjugate of the complex number $\frac{z_1}{z_2}$;

(2) In the complex plane, let points $Z_1$, $Z_2$ correspond to ${z_1}$, ${z_2}$ respectively, and $O$ be the origin. Form a parallelogram with $\overrightarrow{OZ_1}$, $\overrightarrow{OZ_2}$ as adjacent sides. Find the length of the diagonal of this parallelogram.

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