
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
Point \(M\) is the midpoint of chord \(AB\). Chord \(CD\) intersects \(AB\) at point \(M\). A semicircle is constructed on segment \(CD\) as its diameter. Point \(E\) lies on this semicircle, and \(ME\) is perpendicular to \(CD\). Find the angle \(AEB\).

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