
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 \( z_{1} = 3(\cos 330^{\circ} + i \sin 330^{\circ}) \) and \( z_{2} = 2(\cos 60^{\circ} + i \sin 60^{\circ}) \), find: a) \( z_{1} z_{2} \); b) \( \frac{z_{1}}{z_{2}} \); c) \( z_{2}^{4} \); d) \( \sqrt[3]{z_{1}} \).

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