
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 are tossed randomly into bins numbered 1 through 20, such that for each ball, the probability that it lands in bin $i$ is $2^{-i}$ for $i=1,2,\ldots,20$. Find the probability that the balls end up evenly spaced in distinct numbered bins.

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