
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
Given the parabola $y^{2}=2px (p > 0)$ intersects the line $y=2x-4$ to form a chord of length $|AB|=3 \sqrt {5}$,
(I) Find the equation of the parabola;
(II) Let $F$ be the focus of the parabola, find the maximum distance from a point on the circumcircle of $\triangle ABF$ to the line $AB$.

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