
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
In an equilateral triangle \(ABC\), points \(A_1\) and \(A_2\) are chosen on the side \(BC\) such that \(BA_1 = A_1A_2 = A_2C\). A point \(B_1\) is chosen on the side \(AC\) such that \(AB_1 : B_1C = 1 : 2\). Find the sum of the angles \(\angle AA_1 B_1\) and \(\angle AA_2 B_1\).

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