
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
Let the quadratic function $y=ax^{2}+bx+c(a$,$b$,$c$ are constants, $a\neq 0)$, as shown in the table below with 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 set of the inequality $ax^{2}+bx+c \lt 0$ is ______.

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