
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
It is known that the line $l$ intersects the parabola $y^2=8x$ at points $A$ and $B$, and the segment $AB$ is exactly bisected by point $P(2, 2)$.
(1) Find the equation of line $l$;
(2) Determine whether there exist points $C$ and $D$ on the parabola such that $C$ and $D$ are symmetric about line $l$. If they exist, find the equation of line $CD$; if not, explain why.

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