
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 the equation in terms of $x$, $2x^2-(\sqrt{3}+1)x+m=0$, has two roots $\sin \theta$ and $\cos \theta$, where $\theta\in(0,2\pi)$.  
$(1)$ Find the value of $\dfrac{\sin ^{2}\theta}{\sin \theta-\cos \theta}+\dfrac{\cos ^{2}\theta}{\cos \theta-\sin \theta}$.  

$(2)$ Find the value of $m$.

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