
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
a) Someone wrote $n$ letters and sealed them in envelopes without addressing them first. Afterwards, they no longer knew which letter was in which envelope, so they randomly wrote $n$ addresses on the envelopes. What is the probability that at least one of the recipients gets the letter intended for them?

b) What limit does the probability in part a) approach as $n \rightarrow \infty$?

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