
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 the equation $y = ax^2 + bx + c$ is graphed as follows:
- Vertex: $(3, -2)$
- Another Point on Parabola: $(5, 14)$

Calculate the difference, $m-n$, between the zeros $x = m$ and $x = n$ of the quadratic $ax^2 + bx + c$, where $m > n$.

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