
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
Initially, there are some red balls and some black balls in a box. After adding some black balls, the red balls account for one-fourth of the total number of balls. Then, after adding some red balls, the number of red balls becomes two-thirds the number of black balls. If the number of added black balls and red balls is the same, find the original ratio of the number of red balls to black balls in the box.

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