
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
Calculate the sum:
\[
S = \sum_{n=0}^{24} i^n \cos(45n^\circ) 
\]
where $i^2 = -1$.
A) $7 + 6i\sqrt{2}$  
B) $7 - 6i\sqrt{2}$  
C) $6i\sqrt{2} - 1$  
D) $6\sqrt{2} + i$

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