
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
Once upon a time, a team of Knights and a team of Liars met in the park and decided to ride a circular carousel that can hold 40 people (the "Chain" carousel, where everyone sits one behind the other). When they took their seats, each person saw two others: one in front and one behind. Each person then said, "At least one of the people sitting in front of me or behind me belongs to my team." One spot turned out to be free, and they called one more Liar. This Liar said, "With me, we can arrange ourselves on the carousel so that this rule is met again." How many people were on the team of Knights? (A Knight always tells the truth, a Liar always lies).

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