
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
The focus of the parabola $C: y^{2}=4x$ is $F$, and a line $l$ passing through point $F$ intersects $C$ at points $A$ and $B$. The directrix of $C$ intersects the $x$-axis at point $E$. A moving point $P$ satisfies $\overrightarrow{EP}= \overrightarrow{EB}+ \overrightarrow{EA}$.
- (I) Find the equation of the trajectory of point $P$;
- (II) When the area of quadrilateral $EAPB$ is minimized, find the equation of line $l$.

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