
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 the sides $AB$ and $BC$ of an equilateral triangle $ABC$, points $P$ and $Q$ are chosen such that $AP: PB = BQ: QC = 2: 1$. Find $\angle AKB$, where $K$ is the point of intersection of segments $AQ$ and $CP$.

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