
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 side length \( BC \) of triangle \( ABC \) is 12 cm. A circle with radius 10 cm is circumscribed around the triangle. Find the lengths of sides \( AB \) and \( AC \) of the triangle, given that the radius \( OA \) of the circle bisects the side \( BC \) into two equal segments.

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