
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 $y=ax^{2}+bx+c$ with respect to $x$ as shown in the table below, the solutions to the quadratic equation $ax^{2}+bx+c=0$ are ______.

|x|$\ldots $|-3|-2|0|$\ldots $|
|-|-|-|-|-|-|
|y|$\ldots $|0|-3|-3|$\ldots $|

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