
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
Three balls, a red, a green, and a blue ball, are tossed independently into bins numbered with the positive integers such that the probability a ball lands in bin $k$ is $3^{-k}$ for $k=1,2,3,...$. Calculate the probability that all three balls land in different bins.

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