
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
Consider a pyramid with a square base where each side of the base measures 2 units. The lateral faces of the pyramid are equilateral triangles. A cube is positioned within the pyramid such that one face of the cube lies entirely on the base of the pyramid, and the top face of the cube has its vertices touching the lateral faces of the pyramid. Calculate the volume of this cube.

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