
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
On the Island of Misfortune, there are knights, who always tell the truth, and liars, who always lie. One day, $n$ islanders gathered in a room.

The first one said, "Exactly every first person present in this room is a liar."

The second one said, "Exactly every second person present in this room is a liar," and so on.

The person with number $n$ said, "Exactly every $n$-th person present in this room is a liar." How many people could have been in the room?

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