
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
Twelve points are spaced around a $3 \times 3$ square at intervals of one unit. Two of the 12 points are chosen at random. Find the probability that the two points are one unit apart.

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