
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 $ABC$, $BD$ is the median to side $AC$, and $BE$ is the angle bisector of $\angle ABC$ such that $AD = 2DC$. Determine the ratio $\frac{AB}{BC}$ given that $BD$ and $BE$ meet at the same point.
A) $\frac{1}{2}$  
B) 1  
C) 2  
D) 3

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