
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
A traveler visited a village where each person either always tells the truth or always lies. The villagers stood in a circle, and each told the traveler whether the neighbor to their right was truthful. Based on these statements, the traveler was able to unequivocally determine the fraction of liars among the villagers. Determine what this fraction is.

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