
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 $\dfrac{\sqrt{3}\sin(-1200^{\circ})}{\tan\dfrac{11\pi}{3}} - \cos585^{\circ}\cdot\tan\left(-\dfrac{37\pi}{4}\right)$  
(2) Simplify $\dfrac{\cos\left(\alpha- \dfrac{\pi}{2}\right)}{\sin\left(\dfrac{5\pi}{2}+\alpha\right)}\cdot \sin(\alpha-2\pi)\cdot \cos(2\pi-\alpha)$．

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