
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 $A$, $B$, and $C$ are the interior angles of an acute triangle. $\sqrt{3}\sin A$ and $(-\cos A)$ are the roots of the equation $x^{2}-x+2a=0$.  
$(1)$ Find angle $A$.  
$(2)$ If $\frac{1+2\sin B \cos B}{\cos^{2}B-\sin^{2}B}=-3$, find $\tan B$.

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