
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 sphere with volume \( V \) contains a regular tetrahedron, which in turn contains a sphere, and the process continues infinitely. Calculate first the sum of the volumes of the spheres and second the sum of the volumes of the tetrahedrons.

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