
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
In the country of knights (who always tell the truth) and liars (who always lie), 10 people are seated at the vertices of a regular decagon around a round table. Among them, there are liars. A traveler can stand somewhere and ask the seated people: "What is the distance from me to the nearest liar among you?" Everyone then responds to the traveler. What is the minimum number of questions that the traveler must ask to definitively identify who the liars are at the table? (There are no bystanders, and the traveler cannot stand on the table. Consider people as points, and assume that everyone, including the traveler, can accurately measure any distance.)

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