
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
In the Cartesian coordinate system, it is known that the terminal side of an angle $\alpha$ with the origin as the vertex and the non-negative half-axis of the $x$-axis as the initial side passes through the point $(-3,-4)$.  
$(1)$ Find the value of $\frac{sin\alpha}{tan\alpha}$;  
$(2)$ Find the value of $\frac{sin(\alpha+\frac{\pi}{2})\cdot cos(\frac{9\pi}{2}-\alpha)\cdot tan(2\pi-\alpha)\cdot cos(-\frac{3\pi}{2}+\alpha)}{sin(2\pi-\alpha)\cdot tan(-\alpha-\pi)\cdot sin(\pi+\alpha)}$.

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