
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 the ellipse $C$: $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 (a > b > 0)$ has an eccentricity of $\dfrac{\sqrt{3}}{2}$, the line $y=x$ intersects the ellipse $C$ at points $A$ and $B$, the right vertex of the ellipse $C$ is $P$, and it satisfies $|\overrightarrow{PA} + \overrightarrow{PB}| = 4$.
(Ⅰ) Find the equation of the ellipse $C$;
(Ⅱ) If the line $y=kx+m (k \neq 0, m \neq 0)$ intersects the ellipse $C$ at two distinct points $M$ and $N$, and the fixed point $Q(0, -\dfrac{1}{2})$ satisfies $|\overrightarrow{MQ}| = |\overrightarrow{NQ}|$, find the range of the real number $m$.

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