
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 $\sin \theta$ and $\cos \theta$ are the two roots of the equation $x^{2} - (\sqrt{3} - 1)x + m = 0$.

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