
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 a quadratic function $y=ax^{2}+bx+c(a$,$b$,$c$ are constants, $a\neq 0)$, the table below shows some corresponding values of $x$ and $y$.  

| $x$ | $\ldots $ | $-5$ | $-3$ | $1$ | $2$ | $3$ | $\ldots $ |
|-----|-----------|------|------|----|----|----|----------|
| $y$ | $\ldots $ | $-2.79$ | $m$ | $-2.79$ | $0$ | $n$ | $\ldots $ |

Then the solution to the equation $ax^{2}+bx+c=n$ is ______.

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