
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
On a plane with 100 seats, there are 100 passengers, each with an assigned seat. The first passenger ignores the assigned seat and randomly sits in one of the 100 seats. After that, each subsequent passenger either sits in their assigned seat if it is available or chooses a random seat if their assigned seat is taken. What is the probability that the 100th passenger ends up sitting in their assigned seat?

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