
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 $\angle C > 90^\circ$, $AM = MB$, $MD \perp BC$ ($D$ is on $BC$), and $ME \perp AB$ ($E$ is on $AB$, $M$ is the midpoint of $EB$). If the area of $\triangle ABC$ is $30$, find the area of $\triangle BDE$.
A) 7
B) 7.5
C) 8
D) 8.5

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