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

| $x$ | $\ldots $ | $-3$ | $-2$ | $0$ | $1$ | $3$ | $5$ | $\ldots $ |
|-----|-----------|------|------|-----|-----|-----|-----|-----------|
| $y$ | $\ldots $ | $7$  | $0$  | $-8$| $-9$| $-5$| $7$ | $\ldots $ |

Then, when $x=2$, the quadratic function $y=ax^{2}+bx+c$ is $y=$____.

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