
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 101 people participating in a Secret Santa gift exchange. Each person is randomly assigned another person to give a gift to, such that each person gives and receives exactly one gift and no one gives a gift to themselves. What is the probability that the first person neither gives gifts to nor receives gifts from the second or third person? Express your answer as a decimal rounded to five decimal places.

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