
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
On side \( AB \) of triangle \( ABC \), point \( K \) is marked, and on side \( AC \), point \( M \) is marked. Segments \( BM \) and \( CK \) intersect at point \( P \). It turns out that angles \( APB \), \( BPC \), and \( CPA \) are each equal to \( 120^\circ \). Additionally, the area of quadrilateral \( AKPM \) is equal to the area of triangle \( BPC \). Find angle \( BAC \).

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