
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 partial corresponding values of the function $y=ax^{2}+bx+c\left(a\neq 0\right)$ in the quadratic function $y=ax^{2}+bx+c$ are as shown in the table below:

\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & \ldots & -2 & -1 & 0 & 2 & \ldots \\
\hline
y & \ldots & -3 & -4 & -3 & 5 & \ldots \\
\hline
\end{array}
\]

Find the expression of this quadratic function.

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