
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 an island, there are 20 inhabitants. Some of them are knights who always tell the truth, and the others are liars who always lie. Each islander knows exactly who among them is a knight and who is a liar. When a visitor asked how many knights live on the island, the first islander answered: "None", the second: "No more than one", the third: "No more than two", the fourth: "No more than three", and so on, until the twentieth said: "No more than nineteen". How many knights live on the island?

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