
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 $M$. Segments $BM$ and $CK$ intersect at point $P$. It turns out that the angles $APB$, $BPC$, and $CPA$ are each $120^\circ$, and the area of quadrilateral $AKPM$ is equal to the area of triangle $BPC$. Find the angle $BAC$.

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