
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
There are 217 inhabitants on an island, out of which 17 are knights and the remaining 200 are tricksters. One day, a private detective visits the island and decides to determine who is who. He asks each inhabitant to write a list of 200 people they consider to be tricksters. The detective does not know who wrote which list, but he knows that knights honestly wrote down 200 actual tricksters, while tricksters could write down any inhabitants of the island (including themselves). Can the detective always identify, based on the obtained lists, at least 13 inhabitants who are definitely tricksters? All the inhabitants of the island have different names, so a name listed always corresponds to a unique inhabitant.

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