
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
In the Cartesian coordinate system $xOy$, there are points $A(-1, 0)$, $B(0, 2)$, and $C(2, 0)$.
1. Find the equation of the line $l$ that passes through point $C$ and is perpendicular to line $AB$.
2. Find the equation of the circle with center at point $C$ that is tangent to line $AB$.

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