
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
Consider the parabola described by the equation $y = a(x-h)^2 + k$. The vertex of the parabola is at $(3, -9)$, and it passes through the point $(5, 7)$. The equation is in the form $y = ax^2 + bx + c$. Find the difference between the larger and smaller zeros of the equation.

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