
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
**Problem Statement**:
Five standard six-sided dice are rolled. It is known that there are two pairs of dice showing the same number, but different from each other. These four dice are set aside, and the remaining die 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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