
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 the curve C: $y^2=2x-4$.  
(1) Find the equation of the tangent line to curve C at point A $(3, \sqrt{2})$.  
(2) A line $l$ passing through the origin $O$ intersects curve C at two distinct points A and B. Find the equation of the trajectory of the midpoint M of segment AB.

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