
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
The height of a regular square pyramid is twice the length of its base edge. What fraction of the pyramid's volume is the volume of the cube inscribed in the pyramid? (The inscribed cube has four vertices on the lateral edges of the pyramid and four vertices on the base.)

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