
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
There are 16 people in Nastya's room, each of whom either is friends with or hostile to every other person. Upon entering the room, each person writes down the number of friends who are already there, and upon leaving, writes down the number of enemies still remaining in the room. What can the sum of all the recorded numbers be after everyone has first entered and then left the room?

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