
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 hexagonal pyramid \( S A B C D E F \) (with the vertex \( S \)), three points are taken on the diagonal \( A D \), dividing it into 4 equal parts. Sections parallel to the plane \( S A B \) are made through these points. Find the ratios of the areas of the resulting sections.

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