
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 $10$ and height $15$, there are four congruent spheres with radius $r$. Each sphere is tangent to the others (where each sphere touches at least one other), and each is also tangent to the base and the side of the cone. Find the radius $r$ of each sphere.

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