
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 behind the other, all facing the same direction. Among them were three brothers: Peter, Nikolai, and Denis. There were 50 people ahead of Peter, 100 people ahead of Nikolai, and 170 people ahead of Denis. On the command "About-face!" everyone turned in the opposite direction. In doing so, it turned out that in front of one of the brothers now stood four times as many people as in front of another brother. How many recruits might there be in total, including the brothers? List all possible options.

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