
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:
\[
\sum_{x=3}^{45} 2\cos{x}\cos{2}[1 + \csc (x-2) \csc (x+2)]
\]
and express it in a form involving $\theta_1, \theta_2, \theta_3, \theta_4$ where $\theta_n$ are angles in degrees.

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