
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 the curve $C$ at the point $A(3, \sqrt {2})$;
(2) Draw a line $l$ through the origin $O$ intersecting the curve $C$ at two distinct points $A$ and $B$, then find the trajectory equation of the midpoint $M$ of the line segment $AB$.

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