
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
A bag contains 20 balls of three different colors: white, black, and red. There is at least one ball of each color. It turned out that if the number of white balls in the bag is doubled, the probability of drawing a white ball becomes $\frac{1}{5}$ less than the initial probability of drawing a red ball (before doubling the white balls). Find the number of balls of each color.

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