
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 their x-coordinates is $2$.

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

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

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