
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 angle $θ$ is in the interval $(0, \frac{π}{2})$, and it satisfies the condition $sinθ + cosθ = \frac{\sqrt{3} + 1}{2}$, $sinθcosθ = \frac{m}{2}$,  
Find: (I) The value of $\frac{sinθ}{1- \frac{1}{tanθ}} + \frac{cosθ}{1-tanθ}$;  
(II) The value of $m$ and the corresponding value of $θ$.

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