
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 five, standard, six-sided dice is rolled once. What is the probability that there is exactly one triplet without any pairs (i.e., three dice showing the same value and the remaining two dice showing different values, all distinct from the triplet)?

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