
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
An isosceles triangle with a base \(a\) and base angle \(\alpha\) is inscribed in a circle. Additionally, a second circle is constructed such that it touches the first circle and the base of the triangle, with the point of tangency being the midpoint of the base. Find the radius of the second circle. If there are multiple solutions, consider all cases.

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