
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
Arrange $n$ people in a line, and call any two adjacent people "friends." If a subset $A$ of this set of $n$ people satisfies: no two people in $A$ are "friends," then the subset $A$ is called a "bad subset." Find the number of "bad subsets" containing $k$ people in the set of $n$ people.

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