
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 $\theta \in (0, \frac{\pi}{2})$ and satisfies the conditions $\sin \theta + \cos \theta = \frac{\sqrt{3}+1}{2}$ and $\sin \theta \cos \theta = \frac{m}{2}$, find:
1. The value of $\frac{\sin \theta}{1 - \frac{1}{\tan \theta}} + \frac{\cos \theta}{1 - \tan \theta}$;
2. The value of $m$ and the corresponding value of $\theta$.

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