
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 founder of a noble family received a plot of land. Each man in the family, upon his death, divided the land he had equally among his sons. If he had no sons, the land was transferred to the state. No other family members acquired or lost land by any other means. In total, there were 150 people in the family. What is the smallest possible fraction of the original plot that could be received by a family member?

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