
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
The recruits were standing in a row one behind the other, all facing the same direction. Among them are three brothers: Peter, Nikolay, and Denis. There were 50 people ahead of Peter, 100 people ahead of Nikolay, and 170 people ahead of Denis. Upon the command "About-face!", everyone turned to face the opposite direction. As a result, it turned out that the number of people now in front of one of the brothers is four times the number of people in front of another. How many recruits, including the brothers, can there be? List all possible options.

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