
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 $\frac{x^2}{3} + y^2 = 1$, let line $l$ intersect the ellipse at points $A$ and $B$. The distance from the coordinate origin $O$ to line $l$ is $\frac{\sqrt{3}}{2}$. Determine the maximum area of $\triangle AOB$.

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