
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
(1) If $ \frac{\pi}{2} < \alpha < \pi $, and $ \sin \alpha = \frac{4}{5} $, find the value of $ \frac{\sin (2\pi-\alpha)\tan (\pi+\alpha)\cos (-\pi+\alpha)}{\sin ( \frac{\pi}{2}-\alpha)\cos ( \frac{\pi}{2}+\alpha)} $.

(2) Simplify $ \frac{\sin (\alpha+n\pi)+\sin (\alpha-n\pi)}{\sin (\alpha+n\pi)\cos (\alpha-n\pi)} $.

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