
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
Three circles are given. The first circle is centered at point $A$ with radius $r$, and the second, smaller circle is centered at point $B$ with a radius of $\frac{r}{2}$ and intersects the first circle at two points. The center $B$ is located on the diameter of the first circle extended from $A$. The third circle is also centered at $A$ but with a radius of $\frac{3r}{2}$ and intersects the line connecting $A$ and $B$ at point $D$. Points $A$, $B$, and $D$ lie along a straight line with $D$ beyond $B$. If the circles intersect at points $C$ and $E$, where $E$ is beyond $D$ from $A$, determine the degree measure of $\angle CED$.
A) 90
B) 105
C) 120
D) 135
E) 150

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