
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
In a group of \( n \) people, there are \( k \) individuals who each have exactly two acquaintances within the group. Among the remaining \( (n-k) \) members, none of them know each other.

What is the maximum number of handshakes that can occur if the strangers introduce themselves to each other? (The acquaintanceship between two people is considered mutual. During each introduction, the two participating individuals shake hands.)

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