
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 points $A$ and $B$ on the curve $C$: $y=\frac{{x}^{2}}{2}$, the sum of the x-coordinates of $A$ and $B$ is $2$.

(I) Find the slope of line $AB$.

(II) Let $M$ be a point on curve $C$ such that the tangent line to curve $C$ at point $M$ is parallel to line $AB$, and $AM$ is perpendicular to $BM$. Find the equation of line $AB$.

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