
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 Isle of Unluckiness, 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 1 percent of those present in this room are knights."

The second one said: "Exactly 2 percent of those present in this room are knights."

And so on.

The person numbered $n$ said: "Exactly $n$ percent of those present in this room are knights."

How many people could have been in the room if it is known for sure that at least one of them is a knight?

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