
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 using a two-stage process. First, the outcome of a fair coin flip determines the type of selection: if heads, a fair six-sided die is rolled, and the chosen number is 0 if the die roll results in an even number and 1 if the die roll results in an odd number; if tails, the number is chosen uniformly at random from the closed interval $[0,1]$. Two random numbers $x$ and $y$ are selected independently using this method. Calculate the probability that $|x-y| > \tfrac{1}{2}$.

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