
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
Diana and Apollo each roll two six-sided dice and sum their respective results. What is the probability that Diana's sum exceeds Apollo's sum by at least 2?
A) \(\dfrac{1}{6}\)
B) \(\dfrac{47}{432}\)
C) \(\dfrac{83}{432}\)
D) \(\dfrac{1}{3}\)
E) \(\dfrac{1}{2}\)

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