
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
In the Cartesian coordinate system $xOy$, it is known that the center of the circle $x^2+y^2-12x+32=0$ is $Q$. A line passing through point $P(0,2)$ with a slope of $k$ intersects the circle $Q$ at two distinct points $A$ and $B$.

(Ⅰ) Find the range of values for $k$;  
(Ⅱ) When $\overrightarrow{OA} \cdot \overrightarrow{OB} = 28$, find the equation of line $l$;  
(Ⅲ) Determine whether there exists a point $C$ on the y-axis such that $\overrightarrow{CA} \cdot \overrightarrow{CB}$ is a constant value. If it exists, find the coordinates of $C$ and the value of $\overrightarrow{CA} \cdot \overrightarrow{CB}$; if not, explain why.

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