
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 in the same direction. Among them were three brothers: Peter, Nikolai, and Denis. There were 50 people in front of Peter, 100 people in front of Nikolai, and 170 people in front of Denis. When the command "About face!" was given, everyone turned to face the opposite direction. It then turned out that in front of one of the brothers there were four times as many people as in front of another. How many recruits could there be, including the brothers? List all possible variants.

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