
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
Distinct points \( A, B, C, D \) are given such that triangles \( ABC \) and \( ABD \) are equilateral and each has a side length of 10. Point \( E \) lies inside triangle \( ABC \) such that \( EA = 8 \) and \( EB = 3 \), and point \( F \) lies inside triangle \( ABD \) such that \( FD = 8 \) and \( FB = 3 \). What is the area of quadrilateral \( AEDF \)?

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