
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 number $z = \cos{\theta} + i\sin{\theta}$, determine the quadrant in the complex plane that corresponds to the complex number $z$ when $\theta = \frac{4}{3}\pi$.

A) First quadrant
B) Second quadrant
C) Third quadrant
D) Fourth quadrant

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