
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 a faraway kingdom, there are 17 islands, each inhabited by 119 people. The inhabitants of the kingdom 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 counting yourself, are there an equal number of knights and liars on your island?" It turned out that on 7 islands everyone answered "Yes," and on the other islands, everyone answered "No." Then each person was asked: "Is it true that, including you, people of your caste constitute less than half of the island's inhabitants?" This time, on 7 islands everyone answered "No," and on the other islands, everyone answered "Yes." How many liars are there in the kingdom?

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