
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
Try to guess the corresponding proposition about the sphere through the analogy between a circle and a sphere. That is, "In a rectangle inscribed in a circle with radius $R$, the maximum area of a square is $2R^{2}$." The corresponding proposition about the sphere is "In a rectangular solid inscribed in a sphere with radius $R$, the maximum volume of a cube is _______."

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