
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 point $F(-1,0)$ and line $l: x=-4$, if the distance $d$ from a moving point $P$ to line $l$ satisfies $d=2|PF|$,  
(Ⅰ) Find the equation of the trajectory $C$ of point $P$;  
(Ⅱ) On the trajectory $C$, there is a point $P\left( \frac {1}{2}, \frac {3 \sqrt {5}}{4}\right)$, connect $PF$ and intersect trajectory $C$ at another point $Q$. With $P$ as the center and $r=2|PQ|$ as the radius, the chord cut by the circle from line $l: x=-4$ is $AB$, find $|AB|$.

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