
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 a Cartesian coordinate system $xOy$, a line $l$ with slope $k$ passes through the point $A(0,1)$. If line $l$ intersects the circle centered at $C$ with the equation $x^2 + y^2 - 4x + 3 = 0$ at two distinct points $P$ and $Q$,
(Ⅰ) Find the range of values for $k$;
(Ⅱ) Determine whether there exists a real number $k$ such that the vector $\overrightarrow {CP} + \overrightarrow {CQ}$ is collinear with vector $\overrightarrow {m} = (-2,1)$. If such a $k$ exists, find its value; if not, explain why not.

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