
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
Analogous to the theorem in plane geometry: In $\triangle ABC$, if $DE$ is the midline of $\triangle ABC$, then the ratio of the areas $S_{\triangle ADE}$ to $S_{\triangle ABC}$ is $1:4$. If a tetrahedron $A-BCD$ has a midsection $EFG$ parallel to plane $BCD$, then the relationship between the volume of the cut tetrahedron and the original tetrahedron's volume is ___.

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