
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
I have $n$ books, and $k$ of them are my favorites. I place the books randomly on a shelf (so that any order of the $n$ books is equally likely). For which values of $k$ will the probability that the $k$ favorite books end up next to each other be maximized and minimized?

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