
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 knights and liars, a traveler visited his knight acquaintance and found him at a round table with five guests.

- "I wonder, how many of you are knights?" he asked.
- "Why don't you ask each person a question and find out for yourself," one guest suggested.
- "Alright. Tell me each of you, who are your neighbors?" the traveler asked.

Everyone answered the same way.

- "The information is not enough!" said the traveler.
- "But remember, today is my birthday," said one of the guests.
- "Yes, today is his birthday!" said his neighbor.

And the traveler was able to deduce how many knights were at the table. So, indeed, how many knights are there?

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