
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 reports, the traveler was able to determine exactly what proportion of the villagers are liars. Determine what this proportion is.

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