
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 right focus at $F(\sqrt{3}, 0)$, and point $M(-\sqrt{3}, \dfrac{1}{2})$ on ellipse $C$.

(Ⅰ) Find the standard equation of ellipse $C$;

(Ⅱ) Line $l$ passes through point $F$ and intersects ellipse $C$ at points $A$ and $B$. A perpendicular line from the origin $O$ to line $l$ meets at point $P$. If the area of $\triangle OAB$ is $\dfrac{\lambda|AB| + 4}{2|OP|}$ ($\lambda$ is a real number), find the value of $\lambda$.

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