
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 point M on the circle $C: x^2 + y^2 = 2$, with MH perpendicular to the x-axis and H as the foot of the perpendicular, and a point N that satisfies $NH = \frac{\sqrt{2}}{2} MH$, denote the trajectory of the moving point N as curve E.
(Ⅰ) Find the equation of curve E.
(Ⅱ) If AB is a chord of curve E with length 2, and O is the origin of the coordinate system, find the maximum value of the area S of triangle △AOB.

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