
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 person said: "Exactly 1 percent of the people present in this room are liars."

The second person said: "Exactly 2 percent of the people present in this room are liars."

and so on.

The person with number $n$ said: "Exactly $n$ percent of the people present in this room are liars."

How many people could be in the room, given that it is known that at least one of them is a knight?

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