
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
The circles with centers \( O_1 \) and \( O_2 \) intersect at points \( A \) and \( B \). It is known that \( \angle AO_1B = 90^\circ \), \( \angle AO_2B = 60^\circ \), and \( O_1O_2 = a \). Find the radii of the circles.

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