
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 $M(3,y_{0})$ on it, the distance from $M$ to the focus $F$ is equal to $4$.
(I) Find the equation of the parabola $C$;
(II) If a line $l$ passing through the point $(4,0)$ intersects the parabola $C$ at points $A$ and $B$, find the minimum value of the area of $\triangle ABO$.

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