
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
(1) Calculate $$\frac{\sqrt{3}\sin\left(-\frac{20\pi}{3}\right)}{\tan\frac{11\pi}{3}} - \cos\frac{13\pi}{4} \cdot \tan\left(-\frac{37\pi}{4}\right).$$
(2) Given that $\tan\alpha = \frac{4}{3}$, find the values of the following expressions: ① $$\frac{\sin 2\alpha + 2\sin \alpha \cos \alpha}{2\cos 2\alpha - \sin 2\alpha};$$ ② $\sin \alpha \cos \alpha.$

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