
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
In a sphere  $S_0$  we radius  $r$  a cube  $K_0$  has been inscribed. Then in the cube  $K_0$  another sphere  $S_1$  has been inscribed and so on to infinity. Calculate the volume of all spheres created in this way.

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