
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 base of a right prism $A B C D A_1 B_1 C_1 D_1$ is an isosceles trapezoid $A B C D$, in which $AD \parallel BC$ and $AD: BC = n > 1$. A plane is drawn parallel to the diagonal $B_1 D$ through the edge $A A_1$, and another plane is drawn through the edge $BC$ parallel to the diagonal $A_1 C$. Similarly, a plane is drawn parallel to the diagonal $A_1 C$ through the edge $D D_1$, and another plane is drawn through the edge $B_1 C_1$. Find the ratio of the volume of the triangular pyramid bounded by these four planes to the volume of the prism.

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