
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
Let $M$ be a point on side $AB$ of triangle $ABC$ such that $AM = 2MB$. Let $P$ be a point on $AB$ such that $AP = 3PB$. If line segment $MD$ is drawn parallel to $PC$ and intersects $AC$ at $D$, calculate the ratio of the area of triangle $BPD$ to that of triangle $ABC$.

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