
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 horizontal plane can intersect all 6 lateral edges of a prism. If we tilt this plane in such a way that it intersects the upper base near one of the vertices, it will intersect two edges of the upper base while no longer intersecting one of the lateral edges. This increases the number of intersected edges by 1. Similarly, we can increase this number by 1 at the lower base. Thus, we obtain a plane intersecting 8 edges of the prism.

Why can't we achieve more than 8 intersections?

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