
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 $P(2,1)$ and intersects the positive half of the x-axis and y-axis at points $A$ and $B$, respectively, with $O$ as the origin.

1. When the slope $k$ of line $l$ is $-1$, find the area of the circumcircle of triangle $AOB$.
2. When the area of triangle $AOB$ is minimized, find the equation of line $l$.

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