
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 $C$: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$ passes through the point $M(2,1)$, and its eccentricity is $\frac{\sqrt{3}}{2}$.
(Ⅰ) Find the equation of the ellipse $C$;
(Ⅱ) Let $A(0,-1)$, and the line $l$ intersects the ellipse $C$ at points $P$ and $Q$, with $|AP| = |AQ|$. When the area $S$ of $\triangle OPQ$ ($O$ is the origin) is maximized, find the equation of the line $l$.

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