
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 $ABC$, the length of side $AC$ is $2b$, the side $AB$ is $c$, and the angle at vertex $A$ is $60^{\circ}$. Point $M$ is located on the median $BE$ and divides it in the ratio $BM: ME = p: q$. Line $AM$ intersects side $BC$ at point $D$. Find the length of segment $BD$.

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