
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 a moving circle P that is internally tangent to the circle M: (x+1)²+y²=8 at the fixed point N(1,0).
(1) Find the trajectory equation of the moving circle P's center.
(2) Suppose the trajectory of the moving circle P's center is curve C. A and B are two points on curve C. The perpendicular bisector of line segment AB passes through point D(0, 1/2). Find the maximum area of △OAB (O is the coordinate origin).

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