
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 equally among his sons. If a man had no sons, the land was transferred to the state. No other family members gained or lost land in any other way. There were a total of 180 people in the family. What is the smallest possible share of the original plot that a family member could have received?

Answer: \(\frac{1}{2 \cdot 3^{59}}\)

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