
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
$(1)$ Given $cos\alpha=-\frac{4}{5}$, where $\alpha$ is in the second quadrant, find the values of $\sin \alpha$ and $\tan \alpha$;<br/>$(2)$ Given $\tan \alpha =-2$, find the value of $\frac{sin\alpha+cos\alpha}{sin\alpha-3cos\alpha}$.

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