
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 $P(1,4)$ and intersects the positive direction of the $x$-axis at point $A$ and the positive direction of the $y$-axis at point $B$.
1. When the sum $|OA| + |OB|$ is minimized, find the equation of $l$.
2. When the product $|PA| \cdot |PB|$ is minimized, find the equation of $l$.

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