
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
On the segment $A C$, point $B$ is given such that $A B=14$ and $B C=28$. Semicircles are constructed on the segments $A B$, $B C$, and $A C$ as diameters in the same half-plane relative to the line $A B$. Find the radius of the circle that touches all three semicircles.

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