
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 Tenth Kingdom, there are 17 islands, each with 119 inhabitants. The inhabitants are divided into two castes: knights, who always tell the truth, and liars, who always lie. During a population census, each person was first asked, "Not including yourself, are there an equal number of knights and liars on your island?" It turned out that on 7 islands, everyone answered "Yes," while on the rest, everyone answered "No." Then, each person was asked, "Is it true that, including yourself, people of your caste are less than half of the inhabitants of the island?" This time, on some 7 islands, everyone answered "No," while on the others, everyone answered "Yes." How many liars are there in the kingdom?

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