
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 $\tan \alpha$ and $\cos \alpha$ are the two roots of the equation $5x^{2}-mx+4=0$ concerning $x$, and $\alpha$ is in the second quadrant.
(1) Find the values of $\tan \alpha$ and $m$;
(2) Find the value of $\frac{2\sin ^{2}\alpha-\sin \alpha\cdot \cos \alpha+3\cos ^{2}\alpha}{1+\sin ^{2}\alpha }$.

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