
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 village, there are 100 houses. What is the maximum number of enclosed non-overlapping fences that can be built such that each fence encloses at least one house and no two fences enclose the same set of houses?

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