
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 first of two circles passes through the center of the second circle and intersects it at points A and B. The tangent to the first circle, passing through point A, divides the second circle in the ratio \(m:n \ (m<n)\). In what ratio does the second circle divide the first?

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