
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 regular pyramid has a rectangular base with sides of lengths 2 and 3 and has lateral faces that are isosceles triangles. A cube is placed within the pyramid so that one face is on the pyramid's base and three vertices of its top face touch the midpoints of three different lateral faces of the pyramid. Calculate the volume of this cube.

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