
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 planes passing through the vertices of a tetrahedron, parallel to the opposite faces, as well as the centroids of the tetrahedron's faces, form tetrahedra that are similar and similarly oriented to the original. What is the relationship between the volume measurements of these tetrahedra?

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