
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 of knights and liars, a traveler visited his knight friend and saw him sitting at a round table with five guests.

- "I'm curious, how many of you are knights?" he asked.
- "Why don't you ask each one of us some question to find out?" suggested one of the guests.
- "Alright. Tell me, who are your neighbors?" asked the traveler.

Everyone answered this question in the same way.

- "This information is insufficient!" said the traveler.
- "But today is my birthday, don't forget that," said one of the guests.
- "Yes, today is his birthday!" confirmed his neighbor.

With this information, the traveler was able to deduce how many knights were at the table. How many knights are there?

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