
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 $C$: $y^{2}=2px (p > 0)$ with a point $P(4,y_{0})$ on it, and the distance between point $P(4,y_{0})$ and the focus of parabola $C$ is $5$.

(1) Find the equation of the parabola $C$;

(2) If a line passes through a point $M(x_{0},4)$ on parabola $C$ and intersects with parabola $C$ at two other points $D$ and $E$, and $MD \perp ME$, determine whether line $DE$ passes through a fixed point. If it does, find the coordinates of the fixed point; if not, explain why.

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