
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
In an isosceles triangle, the base angle is $\alpha$, and the radius of the inscribed circle is $r$. A line is drawn through the vertex of the base angle and the center of the inscribed circle. Find the segment of this line that lies inside the triangle.

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