
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 the quadratic function $y=ax^{2}+bx+c$, the corresponding values of the independent variable $x$ and the function $y$ are shown in the table below:

| $x$ | $\ldots $ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ | $4$ | $\ldots $ |
|-----|-----------|------|------|----|----|----|----|----|----------|
| $y$ | $\ldots $ | $5$  | $0$  | $-3$ | $-4$ | $-3$ | $0$ | $m$ | $\ldots $ |

$(1)$ The direction of the opening of the parabolic graph is ______, and the value of $m$ is ______;  
$(2)$ Points $P(-3$,$y_{1})$ and $Q(2$,$y_{2})$ are on the graph of the function, where $y_{1}$ ______ $y_{2}$ (fill in $ \lt $, $ \gt $, $=$);  
$(3)$ When $y \lt 0$, the range of values for $x$ is ______;  
$(4)$ The solutions to the quadratic equation in $x$, $ax^{2}+bx+c=5$, are ______.

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