
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 line $l$: $y=4x$ and point $P(6,4)$, point $A$ is a point in the first quadrant and lies on line $l$. Line $PA$ intersects the positive half of the $x$-axis at point $B$.
(1) When $OP \perp AB$, find the equation of the line on which $AB$ lies;
(2) Find the minimum area of $\triangle OAB$, and find the coordinates of $B$ when the area of $\triangle OAB$ is minimum.

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