
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 circle $C$: $x^{2}+y^{2}-4x-14y+45=0$ and point $Q(-2,3)$.
(1) If $M$ is any point on circle $C$, find the maximum and minimum values of $|MQ|$;
(2) If real numbers $m$, $n$ satisfy $m^{2}+n^{2}-4m-14n+45=0$, find the maximum and minimum values of $k= \frac {n-3}{m+2}$.

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