
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 $l$ passing through the origin and a circle $C\_1$: $x^2+y^2-6x+5=0$ intersecting at two distinct points $A$ and $B$.

(1) Find the coordinates of the center of the circle $C\_1$.
(2) Find the equation of the locus $C$ of the midpoint $M$ of the segment $AB$.

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