
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 land of knights (who always tell the truth) and liars (who always lie), 10 people sit at the vertices of a regular decagon at a round table, among whom there are liars. A traveler can stand somewhere and ask those seated: "What is the distance from me to the nearest liar among you?" Each person then answers the question. What is the minimum number of questions the traveler must ask to guarantee finding out who the liars are? (There are no outsiders present, the traveler cannot stand on the table, people are considered as points. Everyone, including the traveler, can measure any distance accurately.)

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