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

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