
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 that $M(4,3)$ is a point on the terminal side of angle $\alpha$.  
$(1)$ Find the values of $\sin \alpha$ and $\tan \alpha$;  
$(2)$ Find the value of $\frac{\cos(\frac{\pi}{2}-\alpha)+2\cos(\pi+\alpha)}{\sin(\pi-\alpha)-\sin(\frac{\pi}{2}+\alpha)}$.

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