
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 based on the outcome of flipping two fair coins. If two heads are flipped, then the chosen number is 0; if a head and a tail are flipped (in any order), the number is 0.5; if two tails are flipped, the number is 1. Another number is chosen independently in the same manner. Calculate the probability that the absolute difference between these two numbers, x and y, is greater than $\frac{1}{2}$.

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