
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 $\tan \alpha=3$, compute: $(1)$<sub> $\dfrac{\sin \alpha+\cos \alpha}{\sin \alpha-\cos \alpha} $ </sub>;

 $(2)$<sub> $\dfrac{1}{{\sin }^{2}\alpha-\sin \alpha\cos \alpha-2{\cos }^{2}\alpha} $ </sub>.

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