
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 the endpoint $B$ of the line segment $AB$ moves on the circle $C_{1}$: $x^{2}+(y-4)^{2}=16$, and the coordinates of endpoint $A$ are $(4,0)$, with $M$ being the midpoint of line segment $AB$,

(Ⅰ) Try to find the equation of the trajectory $C_{2}$ of point $M$;  
(Ⅱ) If the circle $C_{1}$ intersects the curve $C_{2}$ at points $C$, $D$, try to find the length of the line segment $CD$.

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