
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 a line $l$ that passes through two points $A(2, 1)$ and $B(6, 3)$:  
(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 point $(2, 0)$. Find the equation of circle $C$;  
(3) If a tangent line to circle $C$ from point $B$ touches points $S$ and $T$, find the equation of line $ST$.

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