
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
Given two points \( C \) and \( D \) on a semicircle with diameter \( AB \), the line segments \( AC \) and \( BD \) intersect at point \( E \). Given \( AB = 10 \), \( AC = 8 \), \( BD = 5\sqrt{2} \), find the area of triangle \( \triangle ABE \).

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