
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. It is known that there is no three-of-a-kind, but there are exactly two pairs of dice showing the same number. These four dice are set aside, and the remaining two dice are re-rolled. What is the probability that after re-rolling these two dice, at least three of the six dice show the same value?

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