
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 frustum with a height of 8 contains a sphere \(O_1\) with a radius of 2. The center of \(O_1\) is on the axis of the frustum, and \(O_1\) is tangent to the upper base and the lateral surface of the frustum. Another sphere \(O_2\) with a radius of 3 can be placed inside the frustum such that \(O_2\) is tangent to \(O_1\), the lower base, and the lateral surface of the frustum. Determine the maximum number of additional spheres with a radius of 3 that can be placed inside the frustum, excluding \(O_2\).

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