
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]


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There are \( n \) seats in a bus, and tickets have been sold to \( n \) passengers. The Absent-Minded Scientist enters the bus first and, without checking his ticket, takes any available seat. Subsequently, passengers enter one by one. If a passenger finds their assigned seat unoccupied, they take it. If their seat is already taken, they occupy the first available seat they find. Find the probability that the last passenger to enter will sit in their assigned seat.

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