
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 red ball, a green ball, and a blue ball are randomly and independently tossed into bins numbered with positive integers. For each ball, the probability that it is tossed into bin k is 2^(-k) for k = 1, 2, 3, \ldots. Calculate the probability that the blue ball is tossed into a higher-numbered bin than both the red and green balls.

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