
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
The progenitor of a noble family received a plot of land. Each man in the family, upon dying, divided his land equally among his sons. If he had no sons, the land reverted to the state. No other family members acquired or lost any land by any other means. There were 200 people in the family. What is the smallest possible share of the original plot that any family member could receive?

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