
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
\[
\frac{2 \cos ^{2}\left(\frac{9}{4} \pi-\alpha\right)}{1+\cos \left(\frac{\pi}{2}+2 \alpha\right)} - \frac{\sin \left(\alpha + \frac{7}{4} \pi\right)}{\sin \left(\alpha + \frac{\pi}{4}\right)} \cdot \operatorname{ctg}\left(\frac{3}{4} \pi - \alpha\right)
\]

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