
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 lines \( l_{1} \) and \( l_{2} \), which form an angle \( \alpha \) between them, serve as common internal tangents to circles with radii \( R_{1} \) and \( R_{2} \). An external common tangent to the circles intersects lines \( l_{1} \) and \( l_{2} \) at points \( A \) and \( B \) respectively. Find the length of segment \( AB \).

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