
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
In the Cartesian coordinate system $xOy$, consider the set of points
$$
K=\{(x, y) \mid x, y \in\{-1,0,1\}\}
$$

Three points are randomly selected from the set $K$. What is the probability that among these three points, there exist two points whose distance is $\sqrt{5}$?

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