
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 $0 < \alpha < \frac{\pi}{2}$, $\sin \alpha= \frac{2 \sqrt{5}}{5}$.  
$(1)$ Find the value of $\tan \alpha$;  
$(2)$ Calculate the value of $\frac{4\sin (\pi-\alpha)+2\cos (2\pi-\alpha)}{\sin ( \frac{\pi}{2}-\alpha)-\sin \alpha}$.

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