
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: \(z_{1}=3\left(\cos \frac{5 \pi}{4}+i \sin \frac{5 \pi}{4}\right), \quad z_{2}=5\left(\cos \frac{\pi}{2}+i \sin \frac{\pi}{2}\right)\). Find: a) \(z_{1} z_{2}\); b) \(z_{1} / z_{2}\); c) \(z_{1}^{5}\); d) \(\sqrt{z_{1}}\).

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