
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 $l: y=kx-3k+2$ and the curve $C: (x-1)^2+(y+1)^2=4$ ($-1\leq x\leq 1$), when the line $l$ is tangent to the curve $C$, the value of $k$ is \_\_\_\_\_\_, and when the line $l$ and the curve $C$ have only one common point, the range of values for $k$ is \_\_\_\_\_\_.

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