
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 point $P(3, 2)$ and intersects the positive x-axis and y-axis at points $A$ and $B$ respectively.  
(1) If the area of $\triangle OAB$ is 12, find the equation of line $l$;  
(2) Let the area of $\triangle AOB$ be $S$, find the equation of line $l$ when $S$ is minimized.

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