
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
Consider the polynomial \(Q(x) = \cos(x) + 2\sin(x) - \cos(2x) - 2\sin(2x) + \cos(3x) + 2\sin(3x)\). Find the number of \(x\) in the interval \(0 \leq x < 2\pi\) for which \(Q(x) = 0\).
A) 0
B) 1
C) 2
D) 3
E) 4

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