
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 the vertex of angle $\alpha$ is at the origin, the initial side coincides with the non-negative half-axis of the $x$-axis, and the terminal side passes through the point $P(-8, m)$, with $\sin \alpha = -\frac{3}{5}$.  
$(1)$ Find the value of $\tan \alpha$;  
$(2)$ Find the value of $\frac{{2\cos\left(\frac{{3\pi}}{2}+\alpha\right)+\cos(-\alpha)}}{{\sin\left(\frac{{5\pi}}{2}-\alpha\right)-\cos(\pi+\alpha)}}$.

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