
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
Two circles with radii 2 and 6, centered at points \( O_{1} \) and \( O_{2} \) respectively, are externally tangent at point \( C \). A common external tangent and a common internal tangent to the circles are drawn. These tangents intersect at point \( D \). Find the radius of the inscribed circle in triangle \( O_{1} O_{2} D \).

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