
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 Absent-Minded Scientist boards a bus with \( n \) seats. All \( n \) tickets have been sold to \( n \) passengers. The Absent-Minded Scientist is the first to enter the bus and, without looking at his ticket, takes a random seat. Subsequently, each passenger enters one-by-one. If a passenger finds their assigned seat free, they take it. If their seat is occupied, they take the first available free seat they find. What is the probability that the last passenger who boards the bus will sit in their assigned seat?

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