
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 taller right circular cone with a base radius of 4 and a height of 15 are three congruent spheres. Each sphere is tangent to the other two as well as one sphere also touches the apex, and each touches the base and the side of the cone. What is the radius \( r \) of each sphere?
A) \( \frac{12}{5} \)
B) \( 4 \)
C) \( \frac{15}{4} \)
D) \( \frac{16}{5} \)

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