
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
Real numbers between 0 and 1 are chosen in the following manner: A fair coin is flipped. If it lands heads, a fair 6-sided die is rolled and the number chosen is the result of the die divided by 6. If the first flip lands tails, then a number is chosen uniformly at random from the interval [0,1]. Two random numbers x and y are selected independently using this method. What is the probability that |x-y| > 1/2?
A) $\frac{1}{6}$
B) $\frac{1}{4}$
C) $\frac{1}{3}$
D) $\frac{3}{8}$

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