
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
In a company of 39 people, each person is either a knight (always tells the truth) or a liar (always lies). They took turns making the following statements:

- "The number of knights in our company is a divisor of 1";
- "The number of knights in our company is a divisor of 2";
- "The number of knights in our company is a divisor of 3";
- $\ldots$
- "The number of knights in our company is a divisor of 39".

How many knights could there be in this company?

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