
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 an ellipse $C: \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ ($a > b > 0$) with the left focus $F(-2,0)$ and the left vertex $A_1(-4,0)$:
(Ⅰ) Find the equation of ellipse $C$;
(Ⅱ) Given points $P(2,3)$ and $Q(2,-3)$ on the ellipse, and $A$ and $B$ are points on the ellipse which lie on opposite sides of the line $PQ$. If $\angle APQ = \angle BPQ$, determine whether the slope of line $AB$ is a constant value. Please explain your reasoning.

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