
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 regular quadrilateral pyramid \( S A B C D \), a cube is inscribed. All four vertices of one face of the cube lie on the base \( A B C D \) of the pyramid. The vertices of the opposite face of the cube lie on the lateral edges of the pyramid. It is known that \( S A = A B = a \), i.e., the lateral edge of the pyramid is equal to \( a \) and also equal to the side of its base. What is the volume of the cube?

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