
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 boys are dividing their catch. The first boy took \( r \) fish and one-seventh of the remaining fish; the second boy took \( 2r \) fish and one-seventh of the new remaining fish; the third boy took \( 3r \) fish and one-seventh of the new remaining fish, and so on. It turned out that in this way, all the caught fish were divided equally. How many boys were there?

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