
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
For real numbers \( x \), let 
\[ P(x) = 1 + e^{ix} - e^{2ix} + e^{3ix} - e^{4ix} \]
where \( i = \sqrt{-1} \). Determine for how many values of \( x \) with \( 0 \leq x < 2\pi \) does
\[ P(x) = 0 \]?
A) 0  
B) 1  
C) 2  
D) 3  
E) 4

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