
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
In rectangle \(ABCD\) with side \(AD\) of length \(5 \text{ cm}\), point \(P\) lies such that triangle \(APD\) is equilateral. Ray \(AP\) intersects side \(CD\) at point \(E\), and segment \(CE\) measures \(5 \text{ cm}\).

How long is segment \(AE\), and what is the measure of angle \(AEB\)?

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