
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
Find the value of the following expression:
\[
\frac{\sin 8 \alpha+\sin 9 \alpha+\sin 10 \alpha+\sin 11 \alpha}{\cos 8 \alpha+\cos 9 \alpha+\cos 10 \alpha+\cos 11 \alpha} \times \frac{\cos 8 \alpha-\cos 9 \alpha-\cos 10 \alpha+\cos 11 \alpha}{\sin 8 \alpha-\sin 9 \alpha-\sin 10 \alpha+\sin 11 \alpha}.
\]

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