
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
A truncated cone with a height of 8 contains a sphere \( O_{1} \) with a radius of 2. The center of sphere \( O_{1} \) lies on the axis of the truncated cone. Sphere \( O_{1} \) is tangent to the upper base and side surface of the truncated cone. Another sphere \( O_{2} \), with a radius of 3, fits inside the truncated cone such that it is tangent to sphere \( O_{1} \), the lower base, and the side surface of the truncated cone at exactly one point each. Find the number of additional spheres with a radius of 3 that can fit inside the truncated cone, excluding sphere \( O_{2} \).

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