
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
In a regular quadrilateral truncated pyramid \(A B C D A_{1} B_{1} C_{1} D_{1}\), a cross-section \(A B C_{1} D_{1}\) is made. Find the volume ratio of the resulting polyhedra \(\frac{V_{A B C D D_{1} C_{1}}}{V_{A_{1} B_{1} C_{1} D_{1} A B}}\), given that \(A B : A_{1} B_{1} = 3\). Round your answer to two decimal places.

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