
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 functions $f(x) = mx + 2$ and $g(x) = x^2 + 2x + m$, if there exist integers $a$ and $b$ such that the solution set for $a \leq f(x) - g(x) \leq b$ is exactly $[a, b]$, then the value of $a-b$ is $\boxed{-2}$.

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