
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 \( y = ax^2 + bx + c \) has its vertex at \( (3, -3) \) and passes through the point \( (5, 15) \). The zeros of the quadratic \( ax^2 + bx + c \) are at \( x = p \) and \( x = q \), where \( p > q \). Find \( p-q \).

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