
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 $y^{2}=32x$, 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) Given a line $l$: $y=k(x-2)(k > 0)$ intersects the trajectory $E$ at points $A$ and $B$, and point $F(2,0)$, if $|AF|=2|BF|$, find the length of chord $AB$.

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