
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 \(XYZ\) be a triangle with \(\angle XYZ = 40^\circ\) and \(\angle YZX = 60^\circ\). A circle \(\Gamma\), centered at the point \(I\), lies inside triangle \(XYZ\) and is tangent to all three sides of the triangle. Let \(A\) be the point of tangency of \(\Gamma\) with \(YZ\), and let ray \(\overrightarrow{XI}\) intersect side \(YZ\) at \(B\). Determine the measure of \(\angle AIB\).

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