
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

Simplify the expression:

$$
\frac{\cos \left(\alpha+\frac{3}{2} \pi\right)+2 \cos \left(\frac{11}{6} \pi-\alpha\right)}{2 \sin \left(\frac{\pi}{3}+\alpha\right)+\sqrt{3} \sin \left(\frac{3}{2} \pi-\alpha\right)}
$$

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