
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
Complete the following two questions.  
$(1)$ Simplify: $\frac{{\cos(\alpha-\frac{\pi}{2})}}{{\sin(\frac{5\pi}{2}+\alpha)}}\sin(\alpha-2\pi)\cos(2\pi-\alpha)$;  
$(2)$ Given $\tan \alpha =2$, find the value of $\frac{{\sin2\alpha}}{{\sin^2\alpha+\sin\alpha\cos\alpha-\cos2\alpha-1}}$.

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