
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
Six standard six-sided dice are rolled. We are told that there is a triplet and a pair among these dice, but no four-of-a-kind. The triplet and the pair are set aside, and the remaining die is re-rolled. What is the probability that after re-rolling this single die, there is at least a four-of-a-kind or a full house?

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