
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
How many values of \(\theta\) in the interval \(0 < \theta \leq 2\pi\) satisfy the equation
\[
2 - 4\sin\theta + 6\cos2\theta + \sin3\theta = 0?
\]
A) 6
B) 7
C) 8
D) 9
E) 10

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