
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 the obtuse triangle $ABC$ with $\angle B>90^\circ$, $AM=MB$, $MD\perp AC$, $EC\perp AB$, and $F$ is a point on $AC$ such that $EF\perp AC$ ($D$ is on $AC$, $E$ is on $AB$, and $M$ is on $EB$). If the area of $\triangle ABC$ is $36$, determine the area of $\triangle BED$.
A) 9
B) 12
C) 15
D) 18
E) Not uniquely determined

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