
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, where $N > 5$, at least two people have not shaken hands with everyone else. What is the maximum number of people in this group that could have shaken hands with every other person?

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