
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
In the Cartesian coordinate system, given point M(1,0), and P(x,y) is a moving point on the plane. The distance from P to the line x=2 is d, and $$\frac {|PM|}{d} = \frac { \sqrt {2}}{2}$$.
(Ⅰ) Find the equation of the trajectory C of point P;
(Ⅱ) A line l, which does not pass through the origin O, intersects C at points A and B. The midpoint of segment AB is D, and the y-coordinate of the intersection point of line OD with the line x=2 is 1. Find the maximum area of triangle OAB and the equation of line l at this condition.

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