
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
There are 160 balls in total of three colors: red, yellow, and white. If $\frac{1}{3}$ of the red balls, $\frac{1}{4}$ of the yellow balls, and $\frac{1}{5}$ of the white balls are taken out, then 120 balls remain. If $\frac{1}{5}$ of the red balls, $\frac{1}{4}$ of the yellow balls, and $\frac{1}{3}$ of the white balls are taken out, then 116 balls remain. How many red, yellow, and white balls were there originally?

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