
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 \( R \) and \( r \) (\(R > r\)) touch internally at point \( A \). A line is drawn through point \( B \), which lies on the larger circle, and is tangent to the smaller circle at point \( C \). Find the length of \( AB \) if \( BC = a \).

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