
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 $\sin(3\pi + \alpha) = 2\sin\left(\frac{3\pi}{2} + \alpha\right)$, find the values of the following expressions:  
(1) $$\frac{2\sin\alpha - 3\cos\alpha}{4\sin\alpha - 9\cos\alpha}$$;  
(2) $\sin^2\alpha + \sin 2\alpha$.

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