
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 randomly and independently tossed into bins numbered with the positive integers. The probability that a ball lands in bin \( k \) is \( \frac{1}{2^k} \) for \( k = 1,2,3,\ldots \). What is the probability that the red ball is tossed into a higher-numbered bin than both the green and the blue balls?
A) \( \frac{1}{7} \)
B) \( \frac{1}{3} \)
C) \( \frac{2}{7} \)
D) \( \frac{1}{6} \)
E) \( \frac{1}{2} \)

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