
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
Convex quadrilateral $ABCD$ has $AB = 10$, $CD = 15$, diagonals $AC$ and $BD$ meet at $E$, where $AC = 15$. It is given that $\triangle AEB$ and $\triangle DEC$ have equal areas. What is the length of $AE$?
**A)** 5
**B)** 6
**C)** 7.5
**D)** 9
**E)** 10.5

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