
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
A line $l$ passes through the point $P(1,2)$ and intersects the positive half of the $x$-axis at point $A$ and the positive half of the $y$-axis at point $B$. Find the equation of line $l$ that minimizes the area of $\triangle AOB$.

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