
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 were 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. It turned out that in front of one of the brothers now stood four times as many people as 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}
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