
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 $C: x^2 + y^2 - 8y + 12 = 0$, and a line $l$ passing through point $D(-2, 0)$ with a slope of $k$.

(1) Find the equation of circle $E$ whose diameter is the line segment $CD$;  
(2) If line $l$ and circle $C$ are disjoint, find the range of values for $k$.

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