
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 $ABC$, let $D$ be the midpoint of $AC$ and $E$ the midpoint of $AB$. A line segment $DE$ is drawn, and it is given that $DE$ is perpendicular to median $AF$, with $AF$ being 15 and $DE$ being 10. Determine the area of triangle $ABC$.
A) 75
B) 100
C) 125
D) 150
E) 175

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