
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 right circular cone has a larger base radius of 10 cm and a smaller base radius of 5 cm. The height of the truncated cone is 8 cm. Determine the volume of this solid. Furthermore, calculate the volume of the larger complete cone formed by extending the smaller base until it meets the point with the larger base as the radius of the frustum.

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