
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 around a cube such that four vertices of the cube lie on the plane of the base of the cone, and the other four vertices lie on its lateral surface. What is the minimum volume that such a cone can have if the edge length of the cube is \(a\)?

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