
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 following expression:
$$
\frac{\sin (2 \alpha-3 \pi)+2 \cos \left(\frac{7}{6} \pi+2 \alpha\right)}{2 \cos \left(\frac{\pi}{6}-2 \alpha\right)+\sqrt{3} \cos (2 \alpha-3 \pi)}
$$

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