
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, 15 islanders lined up in order of height (from tallest to shortest, with the tallest standing 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." Those standing in positions four through eight said the first phrase, and the rest said the second phrase. How many knights were among these 15 people, given that all the residents are of different heights?

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