
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]


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On the segment \( AC \) of length 12 cm, a point \( B \) is constructed such that \( AB = 4 \) cm. Semicircles are constructed on segments \( AB \) and \( AC \) as diameters in the same half-plane with boundary \( AC \). Calculate the radius of the circle that is tangent to the constructed semicircles and \( AC \).

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