
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 that the line $l$ passes through the point $P(3,4)$<br/>(1) Its intercept on the $y$-axis is twice the intercept on the $x$-axis, find the equation of the line $l$.<br/>(2) If the line $l$ intersects the positive $x$-axis and positive $y$-axis at points $A$ and $B$ respectively, find the minimum area of $\triangle AOB$.

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