
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 of 24 and a height of 18 has a semicircle inscribed in it such that the diameter of the semicircle lies along the base of the triangle. Additionally, a full circle is inscribed in the triangle touching the two equal sides and the base. Determine the radii of both the semicircle and the full circle.
A) 12 and \(\frac{216}{78}\)
B) 12 and \(\frac{108}{42 + 6\sqrt{13}}\)
C) 24 and \(\frac{216}{84}\)
D) 12 and \(\frac{216}{6(\sqrt{13} + 2)}\)

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