
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
Among the five rational numbers $-3$, $-2$, $0$, $+1$, $+3$, any three numbers are selected to find the minimum sum, denoted as $a$, and any three numbers are selected to find the maximum product, denoted as $b$. <br/> $(1)$ Find the values of $a$ and $b$; <br/> $(2)$ If $|x-4|+(y+a)^{2}=0$, find the value of the algebraic expression $\frac{y^{2}}{x}-\frac{1}{2}xy$.

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