
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
Inside a right circular cone with base radius $8$ and height $15$, there are three identical spheres. Each sphere is tangent to the others, the base, and the side of the cone. Determine the radius $r$ of each sphere.
A) $\frac{840 - 300\sqrt{3}}{121}$
B) $\frac{60}{19 + 5\sqrt{3}}$
C) $\frac{280 - 100\sqrt{3}}{121}$
D) $\frac{120}{19 + 5\sqrt{5}}$
E) $\frac{140 - 50\sqrt{3}}{61}$

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