
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 equation of circle C: $x^2+y^2-8x+15=0$, and the equation of line $l$: $y=kx-2$  
① If $l$ is tangent to the circle, find the value of $k$;  
② If there is at least one point on $l$ such that a circle with this point as its center and a radius of 1 has common points with circle C, find the range of values for $k$.

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