
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
Given that \( M \) is the midpoint of side \( AB \) in \( \triangle ABC \), and \( P \) is a point on \( AB \) between \( A \) and \( M \), and \( MD \) is parallel to \( PC \) intersecting \( BC \) at \( D \), find the ratio of the area of \( \triangle BPD \) to the area of \( \triangle ABC \).

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