
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 that the two foci of ellipse $E$ are $(-1,0)$ and $(1,0)$, and it passes through the point $(1, \frac{\sqrt{2}}{2})$.
(I) Find the equation of ellipse $E$;
(II) Let line $l$ pass through $P(-2,0)$ and intersect $E$ at points $A$ and $B$, with $\overrightarrow{PB}=3\overrightarrow{PA}$. If the symmetric points of $A$ and $B$ with respect to the $x$-axis are $C$ and $D$, find the equation of the circumcircle of quadrilateral $ACDB$.

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