
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 the company, there are at least two people.

If there is at least one knight, there are \( m \) liars following each knight. However, everyone cannot be a liar, as in a group of \( m \) people following a liar, there is at least one knight.

The person number \( m+1 \), following an arbitrary knight, is the one who follows as number \( m \) after the first liar following this knight. The first \( m-1 \) people following the first liar after the knight are liars. Therefore, the next person number \( m \) must be a knight. This person will either be the initially chosen knight or another knight. In the first case, \( n = m+1 \), and the company has only one knight. In the second case, the number of knights is more than one, and the whole company is divided into groups, with each group containing one knight and \( m \) liars following him. The number of such groups is \( \frac{n}{m+1} \).

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