
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
A circle is circumscribed around triangle \(ABC\). Let \(A_0\) and \(C_0\) be the midpoints of the arcs \(BC\) and \(AB\), respectively, which do not contain vertices \(A\) and \(C\). It turns out that the segment \(A_0C_0\) is tangent to the circle inscribed in triangle \(ABC\). Find angle \(B\).

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