
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 its focus on the x-axis, and a point $P(4, m)$ on the parabola is at a distance of 5 from the focus.  
(1) Find the equation of the parabola $C$;  
(2) Given point $A(4, 0)$, and $M$ is a moving point on the parabola other than the vertex, is there a vertical line $l$ such that the length of the chord intercepted by the circle with $MA$ as its diameter is always a constant value? If it exists, find the equation of $l$; if not, explain why.

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