
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 the Island of Truth and Lies, there are knights who always tell the truth and liars who always lie. One day, 17 island residents lined up in order of height (from tallest to shortest, with the tallest being first) for a game. Each person had to say one of the following phrases: "There is a liar below me" or "There is a knight above me". In the end, those standing in positions from third to sixth said the first phrase, and the rest said the second phrase. How many knights were among these 17 people, assuming all residents have different heights?

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