
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 centers \( O_1 \) and \( O_2 \) intersect at points \( A \) and \( B \). The first circle passes through the center of the second circle and its chord \( BD \) intersects the second circle at point \( C \), dividing the arc \( ACB \) in the ratio \( AC:CB = n \). In what ratio does point \( D \) divide the arc \( ADB \)?

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