
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 \(I\) be the center of the inscribed circle of triangle \(ABC\), and let \(A^{\prime}, B^{\prime}\), and \(C^{\prime}\) be the symmetric points of \(I\) with respect to lines \(BC\), \(CA\), and \(AB\) respectively. The circumcircle of \(A^{\prime} B^{\prime} C^{\prime}\) passes through \(B\). Find \(\widehat{ABC}\).

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