
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 that line $l$ passes through two points $(2,1)$ and $(6,3)$.
$(1)$ Find the equation of line $l$;
$(2)$ Circle $C$ has its center on line $l$, and passes through points $(2,0)$ and $(3,1)$. Find the equation of circle $C$.

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