
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

$$
\frac{\cos ^{2}\left(\frac{5 \pi}{4}-2 \alpha\right)-\sin ^{2}\left(\frac{5 \pi}{4}-2 \alpha\right)}{\left(\cos \frac{\alpha}{2}+\sin \frac{\alpha}{2}\right)\left(\cos \left(2 \pi-\frac{\alpha}{2}\right)+\cos \left(\frac{\pi}{2}+\frac{\alpha}{2}\right)\right) \sin \alpha}
$$

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