
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
Let \( A \) and \( B \) be two points inside the ring formed by concentric circles of radii \( R \) and \( r \); the distance \( AB \) is equal to 1.

What is the smallest angle under which the segment \( AB \) can be seen from the center of the ring?

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