
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
There are $n$ seats in a bus, and all tickets have been sold to $n$ passengers. The Absent-Minded Scientist enters first and sits in a randomly chosen seat without looking at their ticket. The remaining passengers enter one by one. If a passenger sees that their seat is vacant, they take their seat. If their seat is occupied, they sit in the first available seat. Find the probability that the last passenger to enter will sit in their assigned seat according to their ticket.

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