
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 an island, there are 1000 villages, each with 99 inhabitants. Each inhabitant is either a knight, who always tells the truth, or a liar, who always lies. It is known that the island has exactly 54,054 knights. One day, each inhabitant was asked the question: "Are there more knights or liars in your village?" It turned out that in each village, 66 people answered that there are more knights in the village, and 33 people answered that there are more liars. How many villages on the island have more knights than liars?

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