
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
A pyramid with a triangular equilateral base of side length 2 contains a cube. The cube is placed such that its base is at the bottom of the pyramid and each vertex of the cube’s top face is on a lateral face of the pyramid. Assuming the lateral faces of the pyramid are isosceles triangles with equal leg lengths and the same height, determine the maximum possible volume of the cube.

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