
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 $m, n \in \mathbb{R}$, if line $l: mx + ny - 1 = 0$ intersects the x-axis at point A and the y-axis at point B, and the distance from the origin O to line $l$ is $\sqrt{3}$, find the minimum value of the area $S$ of triangle $AOB$.

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