
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

$$
\frac{2 \cos \left(\frac{\pi}{6}-2 \alpha\right)-\sqrt{3} \sin \left(\frac{5 \pi}{2}-2 \alpha\right)}{\cos \left(\frac{9 \pi}{2}-2 \alpha\right)+2 \cos \left(\frac{\pi}{6}+2 \alpha\right)}=\frac{\operatorname{tg} 2 \alpha}{\sqrt{3}}
$$

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