
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 with a base of \(a\) and an angle \(\alpha\) at the base, an inscribed circle is drawn. Find the radius of a circle that is tangent to both the inscribed circle and the legs of the triangle.

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