
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 real roots of the quadratic equation $x^2 - (\sqrt{3} - 1)x + m = 0$ ($m \in \mathbb{R}$), find:  
(1) The value of $m$;  
(2) The value of $\frac{\cos\theta - \sin\theta\tan\theta}{1 - \tan\theta}$.

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