
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 dying, divided his inherited land equally among his sons. If he had no sons, the land was returned to the state. No other member of the family received or lost any land in any other way. There were 120 people in the family. What is the smallest possible fraction of the original plot that any member of the family could have received?

Answer: $\frac{1}{2 \cdot 3^{39}}$

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