
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
Each of six, standard, six-sided dice is rolled once. What is the probability that exactly three pairs occur (that is, three different pairs of numbers are shown on the dice and no three dice show the same number)?

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