
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 fixed point G(-3, 0), S is a moving point on the circle C: $(x-3)^2+y^2=72$ (with C as the center). The perpendicular bisector of SG intersects SC at point E. Suppose the trajectory of point E is M.  
(1) Find the equation of M;  
(2) Is there a line $l$ with a slope of 1 that intersects the curve M at points A and B, and the circle with AB as its diameter just passes through the origin? If it exists, find the equation of $l$; if not, explain why.

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