
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
In a dice game, three dice are rolled simultaneously, and we can reroll any number of dice (0, 1, 2, or 3) two more times. We win if the same number appears on all three dice after the final roll. What is the best strategy, and what is the probability of winning by following that strategy?

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