
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 \( O_{1}, O_{2} \), and \( O_{3} \) are inside the circle \( O_{4} \) with a radius of 6, touching it internally and touching each other externally. Moreover, the circles \( O_{1} \) and \( O_{2} \) pass through the center of circle \( O_{4} \). Find the radius of circle \( O_{3} \).

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