
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 about $x$, $2x^{2}-( \sqrt {3}+1)x+m=0$, its two roots are $\sin θ$ and $\cos θ$, where $θ∈(0,π)$. Find:
$(1)$ the value of $m$;
$(2)$ the value of $\frac {\tan θ\sin θ}{\tan θ-1}+ \frac {\cos θ}{1-\tan θ}$;
$(3)$ the two roots of the equation and the value of $θ$ at this time.

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