
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 $f\left( \alpha \right)=\frac{\tan (-\alpha -\pi )\sin^2(-\alpha -\pi )}{\sin (\alpha -\frac{\pi }{2})\cos (\frac{\pi }{2}+\alpha )\tan (\pi -\alpha )}$.

$(1)$ Simplify $f\left( \alpha \right)$;                         

$(2)$ If $f\left( \alpha \right)=2$, find the value of $\frac{3\sin \alpha +\cos \alpha }{2\sin \alpha -\cos \alpha }$.

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