
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 stood in a row one after another, all facing the same direction. Among them are three brothers: Peter, Nikolai, and Denis. There were 50 people in front of Peter, 100 in front of Nikolai, and 170 in front of Denis. At the command "About face!", everyone turned to face the opposite direction. After turning, it was found that the number of people now standing in front of one of the brothers is four times the number of people standing in front of another. How many recruits, including the brothers, could there be? List all possible options.

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