
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
Compute the sum \[\cos{30^\circ} + i\cos{120^\circ} + \cdots + i^n\cos{(30 + 90n)^\circ}  + \cdots + i^{8}\cos{750^\circ}\].
A) $\frac{3\sqrt{3}}{2}$ 
B) $2\sqrt{3}$
C) $3\sqrt{3}$
D) $-\sqrt{3}$
E) $0$

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