
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 cone is inscribed in a regular hexagonal pyramid, and another cone is circumscribed around it. Find the difference in volumes between the circumscribed cone and the inscribed cone if the height of the pyramid is \( H \) and the radius of the base of the circumscribed cone is \( R \).

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