
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 that point $A$ is a moving point on the circle $F: (x-4)^{2}+y^{2}=16$, and the coordinates of point $B$ are $(-4,0)$, point $P$ is the midpoint of line segment $AB$.
(Ⅰ) Find the equation of the trajectory $C$ of point $P$.
(Ⅱ) Line $l$ passing through point $(-1,3)$ intersects the trajectory $C$ at points $M$ and $N$, with $|MN|=2 \sqrt {3}$. Find the equation of line $l$.

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