
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
Given twelve points are spaced evenly around the perimeter of a 3 x 3 square, with each placed at the corners and the midpoints of each side, find the probability that two of these points selected at random are exactly 1.5 units apart.

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