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

(Ⅰ) Find the equation of the ellipse $E$;

(Ⅱ) Suppose a moving line $l$ passing through point $P$ 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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