
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
Given a truncated cone with a height of 8, a sphere $O_{1}$ with a radius of 2 tangent to the upper base and the side surface of the cone, and another sphere $O_{2}$ with a radius of 3 tangent to the lower base, the side surface of the cone, and sphere $O_{1}$, calculate the maximum number of additional spheres with a radius of 3 that can be placed inside the truncated cone, excluding sphere $O_{2}$.

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