
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 $6$ and height $15$, are two congruent spheres. Each sphere is tangent to the other sphere, the side and the base of the cone. What is the radius \( r \) of each sphere?
A) \(\frac{6\sqrt{29}}{29}\)
B) \(\frac{12\sqrt{29}}{29}\)
C) \(\frac{18\sqrt{29}}{29}\)
D) \(\frac{24\sqrt{29}}{29}\)

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