
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 the line $l$: $3x+y-6=0$ and the circle $C$: $x^{2}+y^{2}-2y-4=0$.
(1) Find the center and radius of the circle, and calculate the distance from the center to the line $l$.
(2) If they intersect, find the length of the chord cut off by the line on the circle.

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