
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
A rectangle $ABCD$ has $AB = 5$ and $BC = 12$. Within the rectangle, point $E$ is defined where diagonal $AC$ intersects with the perpendicular bisector of $BD$. What is the area of triangle $AED$?
A) 15.25
B) 16.25
C) 17.25
D) 18.25

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