
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 $\frac{3π}{4} \lt \alpha\ \ \lt \pi $, $\tan \alpha +\frac{1}{\tan \alpha}=-\frac{10}{3}$. Find:

1. The value of $\tan \alpha$.
2. The value of $\frac{{\sin \alpha + \cos \alpha}}{{\sin \alpha - \cos \alpha}}$.
3. The value of $2\sin ^{2}\alpha - \sin \alpha \cos \alpha - 3\cos ^{2}\alpha$.

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