
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 two points $A$ and $B$ on the curve $C$: $y=\frac{{x}^{2}}{4}$, with $A(x\_1, y\_1)$ and $B(x\_2, y\_2)$, and $x\_1 + x\_2 = 4$.

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

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