
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, and its initial side lies on the non-negative $x$-axis.  
$(1)$ If the terminal side of angle $\alpha$ passes through point $P(1,3)$, find the value of $\sin \alpha$.  
$(2)$ If $\tan (\pi -\alpha)=-2$, find the value of $\frac{{2\sin \alpha - \cos \alpha}}{{\sin \alpha + 2\cos \alpha}}$.

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