
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 $P(0,-2)$, points $A$ and $B$ are respectively the left and right vertices of the ellipse $E$: $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 (a > b > 0)$. The line $BP$ intersects $E$ at point $Q$, and $\triangle ABP$ is an isosceles right triangle, with $\overrightarrow{PQ} = \dfrac{3}{2} \overrightarrow{QB}$.

$(1)$ Find the equation of $E$;

$(2)$ Suppose a variable line $l$ passes through point $P$ and intersects $E$ at points $M$ and $N$. When the origin $O$ is outside the circle with diameter $MN$, find the range of the slope of line $l$.

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