
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, medians BE and CD intersect at right angles, with lengths BE=10 and CD=15. Triangle ABC also has an angle BAC that is twice angle BCA. Find the area of triangle ABC.
A) 50  
B) 75  
C) 100  
D) 125  
E) 150

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