
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 circle $C: (x-1)^2 + (y-2)^2 = 25$ and a line $l: kx-y-5k+4=0$.
(1) If the line $l$ bisects the circle $C$, find the value of $k$.
(2) If the line $l$ intersects the circle $C$ and the chord length is $6$, find the value of $k$.

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