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

| $x$ | $\ldots $ | $-3$ | $-2$ | $-1$ | $0$ | $3$ | $\ldots $ |
|-----|-----------|------|------|------|----|-----|-----------|
| $y$ | $\ldots $ |      | $-11$| $9$  | $21$| $9$ | $\ldots $ |

Fill in the blanks according to the table:
1. The direction of the opening of the graph of the function is ______, and the axis of symmetry is ______;
2. The range of positive roots $x$ of the equation $ax^{2}+bx+c=0$ is ______;
3. The solution set of the inequality $ax^{2}+bx+c \gt 21$ is ______.

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