
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
A circle with equation $x^2+y^2=1$ intersects the x-axis at two points A and B. Any point P on the curve C satisfies $|PA|+|PB|=2\sqrt{2}$, with O being the origin of the coordinate system.
(I) Find the equation of the curve C;
(II) If a tangent line of the circle intersects the curve C at two points M and N, find the maximum area of triangle OMN.

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