
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
Five individuals are assigned to five specific seats, but they do not know their assigned numbers. When these five individuals sit randomly in these five seats, find:
(1) The probability that exactly 3 out of the 5 individuals sit in their assigned seats.
(2) If the probability that all 5 individuals sit in their assigned seats is not less than $\frac{1}{6}$, what is the maximum number of people who can sit in their assigned seats?

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