
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
Let A and B be two points on the curve $C: y= \frac {x^{2}}{4}$. The sum of the x-coordinates of A and B is 4.  
(1) Find the slope of line AB;  
(2) Let M be a point on curve C, the tangent at M is parallel to line AB, and $AM \perpendicular BM$. Find the equation of line AB.

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