
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 moving line $l$ that passes through the origin and a circle $C_{1}$: $x^{2}+y^{2}-6x+5=0$.
(1) Find the range of the slope $K$ of line $l$ when it intersects with the circle;
(2) When $l$ intersects with the circle at two distinct points $A$ and $B$, find the trajectory equation of the midpoint $M$ of line segment $AB$.

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