
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 line one behind the other, 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. Upon the command "About-face!" everyone turned to face the opposite direction. It turned out that there were now four times as many people standing in front of one of the brothers as there were 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