
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
Two congruent circles are centered at points \(A\) and \(B\) such that each circle's center lies on the circumference of the other circle. The line through both \(A\) and \(B\) is extended to intersect the circles at points \(C\) and \(D\) respectively. If the common chord of the two circles is the perpendicular bisector of segment \(AB\), and the circles intersect at two points, one of which is \(E\). If \(\angle CEB\) is a right angle, what is 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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