
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 $cos(\pi+\alpha)=-\frac{3}{5}$.  
$(1)$ Find the values of $sin(\frac{\pi}{2}+\alpha)$ and $\cos 2\alpha$;  
$(2)$ If $\alpha\in(\frac{3\pi}{2},2\pi)$, find the values of $sin(\alpha-\frac{\pi}{4})$ and $tan\frac{\alpha}{2}$.

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