
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
A pyramid is cut by a plane parallel to its base. When the cutting plane respectively bisects the pyramid's lateral edges, lateral surface area, and volume, the corresponding cross-sectional areas are $S_1$, $S_2$, and $S_3$. Determine the relationship among the areas $S_1$, $S_2$, and $S_3$.

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