
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 right $\triangle ABC$ with hypotenuse $\overline{AB}$, we have $AC = 9$, $BC = 40$, and $\overline{CD}$ is the altitude to $\overline{AB}$. If $\omega$ is the circle having $\overline{CD}$ as diameter and $E$ is a point on hypotenuse $\overline{AB}$ such that $\overline{AE}$ is tangent to circle $\omega$, find the length of $\overline{AE}$.

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