
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 are told there is no four-of-a-kind, but there is a pair of dice showing the same number. These two dice are set aside, and the other three dice are re-rolled. What is the probability that after re-rolling these three dice, at least four of the five dice show the same value?

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