
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 length of segment \(AB\) is \(2r\). We draw firstly a circle with center \(A\) and radius \(r\), and secondly a circle with radius \(r\) that is tangent to segment \(AB\) at point \(B\). What angle do the common tangents to these two circles enclose with segment \(AB\)?

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