
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
A parabola, given by the equation $y^{2}=2px (p > 0)$, has a focus that lies on the line $l$. This line intersects the parabola at two points, $A$ and $B$. A circle with the chord $AB$ as its diameter has the equation $(x-3)^{2}+(y-2)^{2}=16$. Find the value of $p$.

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