
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 an ellipse $E$ with foci at $(-1, 0)$ and $(1, 0)$, and it passes through the point $(1, \frac{\sqrt{2}}{2})$.

(Ⅰ) Find the equation of ellipse $E$;  
(Ⅱ) A line $l$ passing through $P(-2, 0)$ intersects $E$ at points $A$ and $B$, and $\overrightarrow{PB} = 3\overrightarrow{PA}$. Let the points $A$ and $B$ be symmetric to the x-axis at points $C$ and $D$ respectively. Find the equation of the circumscribed circle of quadrilateral $ACDB$.

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