
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
\[\frac{4 \cos ^{2}(\alpha-\pi)-4 \sin ^{2}\left(\frac{3}{2} \pi-\frac{\alpha}{2}\right)+3 \cos ^{2}\left(\frac{5}{2} \pi-\alpha\right)}{4 \sin ^{2}\left(\frac{\pi}{2}+\frac{\alpha}{2}\right)-\cos ^{2}\left(\frac{7}{2} \pi-\alpha\right)}=\operatorname{tg}^{4} \frac{\alpha}{2}\]

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