
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 $A(-2,0)$, $B(2,0)$, and $P(x,y)$ satisfying the product of the slopes of $PA$ and $PB$ is $-\frac{3}{4}$.  
$(1)$ Find the equation of the locus $C$ of $P$.  
$(2)$ Let $l_{1}$ and $l_{2}$ be two lines passing through the same point $D$ inside $C$. $l_{1}$ intersects the ellipse at $MN$, and $l_{2}$ intersects the ellipse at $EF$, with $MNEF$ forming a cyclic quadrilateral. Find the sum of the slopes of these two lines.

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