
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
When the value of $x$ is different, the value of the polynomial $ax-b$ (where $a$ and $b$ are constants) is also different, as shown in the table below:

| $x$ | $-3$ | $-2$ | $-1$ | $0$ | $1$ |
|-----|------|------|------|-----|-----|
| $ax-b$ | $4$ | $2$ | $0$ | $-2$ | $-4$ |

Determine the solution to the equation $ax=b-2$ in terms of $x$.

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