
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 that M is any point on the circle C: $x^2+y^2-4x-14y+45=0$, and point Q is at $(-2,3)$.
(Ⅰ) If P $(a, a+1)$ is on circle C, find the length of segment PQ and the slope of line PQ;
(Ⅱ) Find the maximum and minimum values of $|MQ|$.

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