
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
Let \( A, B, C, D \) (written in the order from left to right) be four equally-spaced collinear points. Let \( \omega \) and \( \omega^{\prime} \) be the circles with diameters \( AD \) and \( BD \), respectively. A line through \( A \) that is tangent to \( \omega^{\prime} \) intersects \( \omega \) again at point \( E \). If \( AB = 2\sqrt{3} \text{ cm} \), what is \( AE \)?

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