
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
Given that $\frac{\pi }{2} < \alpha < \pi , \tan \alpha - \frac{1}{\tan \alpha }=-\frac{8}{3}$.

(1) Find the value of $\tan \alpha$;

(2) Find the value of $g(\alpha)= \frac{\sin (\pi+\alpha)+4\cos (2\pi+\alpha)}{\sin ( \frac{\pi}{2}-\alpha)-4\sin (-\alpha) }$.

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