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

(1) Find the value of the real number $m$;

(2) Find the roots of the equation and their corresponding values of $\alpha$.

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