
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
Given two balls, one blue and one yellow, are randomly and independently tossed into bins numbered with positive integers such that for each ball, the probability that it lands in bin $k$ is $3^{-k}$ for $k=1, 2, 3, \ldots$, find the probability that the blue ball is tossed into a higher-numbered bin than the yellow ball.

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