
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 a convex quadrilateral $ABCD$, sides $AB = 10$ and $CD = 15$. Diagonals $AC$ and $BD$ intersect at point $E$. If $AC = 18$ and the area of $\triangle AED$ is twice the area of $\triangle BEC$, determine the length of $AE$.
- **A)** 10
- **B)** 11
- **C)** 12
- **D)** 13
- **E)** 14

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