
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
The corresponding values of the abscissa $x$ and ordinate $y$ of some points on the parabola $y=ax^{2}+bx-4$ are shown in the table below:<br/>

| $x$ | $\ldots $ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $\ldots $ |
|-----|-----------|------|------|----|----|----|----------|
| $y$ | $\ldots $ | $0$  | $-4$ | $-4$ | $0$ | $8$ | $\ldots $ |

Fill in the blanks or find the values according to the table above:<br/>
$(1)$ The coordinates of the intersection points of the parabola and the $y$-axis are ______;<br/>
$(2)$ Find the values of $a$ and $b$;<br/>
$(3)$ When $x=-3$, the value of $y$ is ______.

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