
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
$$\frac{\operatorname{tg}\left(\frac{\pi}{4}-\frac{\alpha}{2}\right)\left(1-\cos \left(\frac{3}{2} \pi-\alpha\right)\right) \cos ^{-1} \alpha - 2 \cos 2 \alpha}{\operatorname{tg}\left(\frac{\pi}{4}-\frac{\alpha}{2}\right)(1+\sin (4 \pi+\alpha)) \cos ^{-1} \alpha + 2 \cos 2 \alpha} = \operatorname{tg}\left(\frac{\pi}{6}+\alpha\right) \operatorname{tg}\left(\alpha-\frac{\pi}{6}\right)$$

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