
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 regular tetrahedron, we draw the midlines on the base face. We then connect the midpoints of each midline with the vertices of the side faces parallel to the midline. What fraction of the volume of the tetrahedron is the common volume of the three tetrahedra obtained in this way?

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