
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 a base radius of $5$ and a revised height of $15$, three congruent spheres are positioned such that each is tangent to the others and also to the base and sides of the cone. Determine the radius $r$ of each sphere.
A) $\frac{118.125 - 62.5\sqrt{3}}{16.0625}$
B) $\frac{118.125 - 62.5\sqrt{3}}{18.0625}$
C) $\frac{118.125 - 62.5\sqrt{3}}{19.0625}$
D) $\frac{118.125 - 62.5\sqrt{3}}{20.0625}$
E) $\frac{118.125 - 62.5\sqrt{3}}{22.0625}$

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