
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 blue ball and a yellow ball are independently tossed into bins numbered with the positive integers. The probability that a ball is tossed into bin $k$ is $3^{-k}$ for $k = 1,2,3,...$. What is the probability that the blue ball is tossed into a higher-numbered bin than the yellow ball?
A) $\frac{1}{8}$
B) $\frac{7}{16}$
C) $\frac{3}{8}$
D) $\frac{1}{4}$

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