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

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