
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 $2x^2 - (\sqrt{3}+1)x + m = 0$ with roots $sin\theta$ and $cos\theta$, where $\theta \in (0, \frac{\pi}{2})$,
1. Find the value of the real number $m$;
2. Find the value of $\frac{sin\theta}{1 - cot\theta} + \frac{cos\theta}{1 - tan\theta}$.

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