
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, inclusive, are chosen in the following way: A six-sided fair die is rolled. If the result is 1 or 2, the number chosen is 0; if the result is 3 or 4, the number chosen is 1; if the result is 5 or 6, the number is chosen uniformly at random from the closed interval $[0,1]$. Two random numbers $x$ and $y$ are chosen independently using this method. What is the probability that $|x-y| > \tfrac{1}{2}$?
A) $\frac{1}{6}$
B) $\frac{1}{4}$
C) $\frac{7}{12}$
D) $\frac{2}{3}$

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