
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
A rectangle is constructed by reflecting an isosceles triangle with a base of 24 and height of 10 over its base, where the diameter of an inscribed semicircle lies along the base of the triangle. What is the radius of the semicircle?
A) $\frac{50}{11}$
B) $6$
C) $\frac{55}{11}$
D) $\frac{60}{11}$
E) $5\frac{1}{2}$

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