
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 $A(0,2)$ is a fixed point inside the circle $C$: $x^{2}+y^{2}=16$, $D$ is a moving point on the circle, and $P$ is the midpoint of the line segment $AD$, find:
1. The equation $E$ of the curve on which point $P$ lies;
2. The length of the line segment $MN$, where points $M$ and $N$ are the intersections of the curve $E$ and the line passing through point $A$ with a slope of $-\frac{3}{4}$.

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