
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 the midpoint of side AB of triangle ABC. Let P be a point on AB between M and B, and let MD be drawn parallel to PC and intersecting BC 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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