
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
Given a room containing N people, where N > 4, exactly two people have not shaken hands with everyone else in the room, find the maximum number of people in the room that could have shaken hands with everyone else.

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