
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 second person in this room is a liar."

The second one said: "Exactly every third person in this room is a liar."

and so on.

The person with number $n$ said: "Exactly every $(n - 1)$-th person in this room is a liar."

How many people could be in the room, knowing that not all of them are liars?

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