
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]


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In a tetrahedron, planes are passed through each edge and the midpoint of the opposite edge. Into how many parts do these planes divide the tetrahedron, and what is the ratio of the volumes of these parts to the volume of the tetrahedron?

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