
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 two points $(2, 1)$ and $(6, 3)$.  
(1) Find the equation of line $l$.  
(2) The center of circle $C$ lies on line $l$, and it is tangent to the x-axis at the point $(2, 0)$. Find the equation of circle $C$.

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