
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 \(xOy\), the set of points \(K=\{(x, y) \mid x, y=-1,0,1\}\). Three points are randomly selected from \(K\). What is the probability that the distance between any two of these three points does not exceed 2?

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