
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 a non-regular pentagonal prism, and another in the shape of a regular quadrilateral pyramid, whose height is half the length of its base side. During the night, mice gnawed away all the particles of cheese located within 1 cm of each vertex of these polyhedra. The gnawed pieces of cheese did not overlap. Which farmer suffered greater damage and by what factor is the damage greater?

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