
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
Five standard six-sided dice are rolled. We determine there are exactly two pairs of dice showing the same numbers but different from each other. The fifth die, which does not match any of the numbers in the two pairs, is re-rolled. What is the probability that after re-rolling this die, at least three of the five dice show the same value?

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