
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
One farmer made cheese in the shape of an irregular pentagonal prism, while another made it in the shape of a regular quadrangular pyramid, with a height that is half the length of a side of the base. During the night, mice ate away all parts of the cheese from all vertices of these polyhedra that were within 1 cm of each corresponding vertex. The eaten pieces of cheese had no common particles. Which of the farmers suffered greater damage and by how much?

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