
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
Let $U$ be a square with side length 1. Two points are randomly chosen on the sides of $U$. Find the value of the probability that the distance between these two points is at least $\frac{1}{2}$ in the form $\frac{a - b \pi}{c}\left(a, b, c \in \mathbf{Z}_{+}, (a, b, c)=1\right)$.

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