
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
Find three numbers such that if each gives a certain specified fraction of itself to the next one, after giving to each other, they will be equal. Specifically, let the first number give one-third of its value to the second, the second gives one-quarter of its value to the third, and the third gives one-fifth of its value to the first. Determine the series of positive integer solutions.

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