
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 parabola with equation $y=ax^2+bx+c$ is graphed below with its vertex at $(1, -2)$ and another point on the parabola being $(3, 10)$. Determine the difference $m-n$ where $x=m$ and $x=n$ are the zeros of the quadratic $ax^2 + bx + c$, with $m>n$.

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