
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 nuts. The first boy took 3 nuts and one-fifth of the remaining nuts; the second boy took twice 3 nuts and one-fifth of the new remainder; the third boy took three times 3 nuts and one-fifth of the next remainder, and so on. How many boys were there if, as a result of such division, each received an equal number of nuts?

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