
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
Medians $BD$ and $CE$ of triangle $ABC$ intersect at an angle of $30^\circ$. Median $BD$ has a length of $10$ units, and $CE$ has a length of $15$ units. Determine the area of triangle $ABC$.
A) 40
B) 45
C) 50
D) 55
E) 60

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