
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 $C$: $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 (a > b > 0)$, with its foci being $F_1$ and $F_2$. A line passing through $F_1$, denoted as $l$: $x + my + \sqrt{3} = 0$, intersects the ellipse $C$ at points $A$ and $B$, and the eccentricity of the ellipse is $e = \dfrac{\sqrt{3}}{2}$;  
(Ⅰ) Find the equation of the ellipse $C$;  
(Ⅱ) If there exists a point $M$ on the ellipse such that $2\overrightarrow{OM} = \overrightarrow{OA} + \sqrt{3}\overrightarrow{OB}$, find the equation of the line $l$.

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