
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
Calculate the value of the following expression:

$$
\frac{\sin \left(2 \pi+\frac{\alpha}{4}\right) \operatorname{ctg} \frac{\alpha}{8}-\cos \left(2 \pi+\frac{\alpha}{4}\right)}{\cos \left(\frac{\alpha}{4}-3 \pi\right) \operatorname{ctg} \frac{\alpha}{8}+\cos \left(\frac{7}{2} \pi-\frac{\alpha}{4}\right)}
$$

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