
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 $C: \dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1 (a > b > 0)$ passes through the point $M(2,1)$, and the eccentricity is $\dfrac{\sqrt{3}}{2}$.

(Ⅰ) Find the equation of ellipse $C$;

(Ⅱ) If the line $l_{1}$ passing through the origin intersects the ellipse $C$ at points $P$ and $Q$, and there exists a point $M$ on the line $l_{2}: x - y + 2\sqrt{6} = 0$ such that $\triangle MPQ$ is an equilateral triangle, find the equation of line $l_{1}$.

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