
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
The frustum \(O_{1} O_{2}\) has top and bottom radii \(r_{1}\) and \(r_{2}\) respectively, with height \(h\). With \(O_{1}\) as the vertex, the frustum's volume outside the cone with base radius \(r_{2}\) but within the cone with base radius \(r_{1}\) is to be found. What is the volume of the part of the frustum \(O_{1} O_{2}\) that is outside the cone with vertex \(O_{1}\) and base radius \(r_{2}\), yet also outside the cone with vertex \(O_{2}\) and base radius \(r_{1}\)?

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