
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 semicircle is inscribed in an isosceles triangle with base $20$ and height $12$ so that the diameter of the semicircle is contained in the base of the triangle. What is the radius of the semicircle?
A) $6$
B) $10$
C) $\dfrac{60}{5 + \sqrt{61}}$
D) $12\sqrt{3}$
E) $\dfrac{10\sqrt{3}}{3}$

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