
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 $C$ passes through two points $M(-3,3)$ and $N(1,-5)$, and the center of the circle $C$ lies on the line $2x-y-2=0$.
- (I) Find the standard equation of the circle $C$;
- (II) A line $l$ passes through the point $(-2,5)$ and intersects the circle $C$ at two distinct points $A$ and $B$. If the slope $k$ of line $l$ is greater than $0$, find the range of $k$.

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