
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
In a box, there are already some red balls and black balls. After putting in some black balls, the red balls account for one-fourth of the total number of balls. After putting in some more red balls, the number of red balls is half the number of black balls. If the number of black balls and red balls added are the same, what is the ratio of the original number of red balls to black balls in the box?

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