
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 points A, B, and C on the ellipse $W: x^2 + 2y^2 = 2$ with O being the origin of the coordinate system.
(Ⅰ) If the line containing A and C has the equation $y = x + 1$, find the length of AC.
(Ⅱ) Let P be a point on segment OB such that $|OB| = 3|OP|$. If P is the midpoint of AC, determine whether the area of triangle OAC is constant and provide the reasoning.

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