
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
Triangle \( \triangle ABC \) is inscribed in circle \( O \), and \( AB > AC > BC \). Point \( D \) is on the arc \( BC \). Perpendiculars are drawn from point \( O \) to \( AB \) and \( AC \), intersecting \( AD \) at points \( E \) and \( F \), respectively. Rays \( BE \) and \( CF \) intersect at point \( P \). When \( BP = PC + PO \), find \( \angle BAC \).

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