
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 a parabola $C$ with its vertex at the origin and focus on the $x$-axis. There is a point $P(4, m)$ on the parabola, and the distance between $P$ and the focus is $6$.

(I) Find the equation of parabola $C$.
(II) If parabola $C$ intersects with line $l$ at two distinct points $A$ and $B$, and the midpoint of $AB$ has coordinates $(2, 2)$, find the equation of line $l$.

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