
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 $C$ with its left and right foci at $F_{1}(-\sqrt{3},0)$ and $F_{2}(\sqrt{3},0)$, respectively, and the ellipse passes through the point $(-1, \frac{\sqrt{3}}{2})$.

(Ⅰ) Find the equation of the ellipse $C$;  
(Ⅱ) Given a fixed point $A(1, \frac{1}{2})$, a line $l$ passing through the origin $O$ intersects the curve $C$ at points $M$ and $N$. Find the maximum area of $\triangle MAN$.

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