
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 and ordinate of some points on the parabola $y=ax^{2}+bx+c$ are shown in the table below:<br/>

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

From the table, it can be inferred that the solutions of $ax^{2}+bx+c=0$ are ______.

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