3. Given a cube $A B C D A_{1} B_{1} C_{1} D_{1}$. What is the smaller part of the volume separated from it by a plane passing through the midpoint of edge $A D$ and points $X$ and $Y$ on edges $A A_{1}$ and $C C_{1}$ such that $A X: A_{1} X=C Y: C_{1} Y=1: 7 ?$
Provide the answer in the form of a proper fraction, do not round.

Example of answer format: $13 / 81$

Answer: $25 / 192$

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