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

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