
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 Knights and Knaves, knights always tell the truth, and knaves always lie. One day, a traveler questioned seven inhabitants of the island.

- "I am a knight," said the first.
- "Yes, he is a knight," said the second.
- "Among the first two, at least 50% are knaves," said the third.
- "Among the first three, at least 65% are knaves," said the fourth.
- "Among the first four, at least 50% are knights," said the fifth.
- "Among the first five, at least 40% are knaves," said the sixth.
- "Among the first six, at least 65% are knights," said the seventh.

Determine how many knights there are among them.

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