
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
From each point on the parabola $y^{2}=16x$, perpendiculars are drawn to the $x$-axis, and the midpoint of these perpendicular segments traces a path $E$.  
(Ⅰ) Find the equation of the trajectory $E$;  
(Ⅱ) If a line $l$ passing through the point $P(3,2)$ intersects the trajectory $E$ at points $A$ and $B$, and point $P$ is the midpoint of chord $AB$, find the equation of line $l$.

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