
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
One of the adjacent angles with vertex $A$ is twice as large as the other. Circles with centers $O_1$ and $O_2$ are inscribed in these angles. Find the angles of triangle $O_1AO_2$ if the ratio of the radii of the circles is $\sqrt{3}$.

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