
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 table shows the values of a student solving the algebraic expression $ax^{2}+bx(a$,$b$ are constants). According to the data in the table, it can be concluded that the roots of the equation $ax^{2}+bx=6$ are ______$.

| $x$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ | $\ldots $ |
|-----|------|------|----|-----|-----|-----|-----------|
| $ax^{2}+bx$ | $6$ | $2$ | $0$ | $0$ | $2$ | $6$ | $\ldots $ |

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