
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 triangle $ABC$ with $\angle B > 90^\circ$, point $M$ is on side $AC$ such that $AM = 3 \cdot MC$, and segments $MD \perp AB$ and $ED \perp AB$ (where points $D$ and $E$ are on side $AB$). If the area of triangle $ABC$ is $36$, find the area of triangle $EMD$.
A) $\frac{3}{8}$
B) $\frac{9}{8}$
C) $\frac{12}{8}$
D) $\frac{18}{8}$
E) Not uniquely determined

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