
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 touch internally. A line passing through the center of the larger circle intersects it at points \( A \) and \( D \), and intersects the smaller circle at points \( B \) and \( C \). Find the ratio of the radii of the circles, given that \( AB : BC : CD = 3 : 7 : 2 \).

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