
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
Design a game with $6$ balls (no distinction other than color) that satisfies the following conditions: the probability of drawing a white ball is $\frac{1}{2}$, the probability of drawing a red ball is $\frac{1}{3}$, and the probability of drawing a yellow ball is $\frac{1}{6}$. Determine the number of white balls, red balls, and yellow balls that should be used.

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