
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
\[ 4.46 \frac{\operatorname{ctg}^{2}(2 \alpha-\pi)}{1+\operatorname{tg}^{2}\left(\frac{3 \pi}{2}-2 \alpha\right)}-3 \cos ^{2}\left(\frac{5 \pi}{2}-2 \alpha\right) = 4 \sin \left(\frac{\pi}{6}-2 \alpha\right) \sin \left(\frac{\pi}{6}+2 \alpha\right). \]

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