
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 an isosceles right triangle $ABC$ with $\angle B = 90^\circ$, $AB = BC = a$, $M$ is the midpoint of $AC$, $MD \perp AC$, and $E$ is the midpoint of $AB$. Find the area of $\triangle ADE$ if the area of $\triangle ABC$ is $50$.
A) $10\sqrt{2}$
B) $12.5$
C) $25$
D) $\frac{25\sqrt{2}}{2}$
E) $25\sqrt{2}$

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