
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 \( ABC \) be a triangle, and let \( D, E \), and \( F \) be the midpoints of sides \( BC, CA \), and \( AB \), respectively. Let the angle bisectors of \( \angle FDE \) and \( \angle FBD \) meet at \( P \). Given that \( \angle BAC = 37^\circ \) and \( \angle CBA = 85^\circ \), determine the degree measure of \( \angle BPD \).

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