
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
Jason rolls three fair standard six-sided dice. Then he looks at the rolls and chooses a subset of the dice (possibly empty, possibly all three dice) to reroll if at least one die shows a 1. After rerolling, he wins if and only if the sum of the numbers face up on the three dice is exactly 8. Jason always plays to optimize his chances of winning. What is the probability that he chooses to reroll exactly two of the dice?
- **A)** $\frac{75}{1296}$
- **B)** $\frac{5}{216}$
- **C)** $\frac{1}{6}$
- **D)** $\frac{1}{36}$
- **E)** $\frac{42}{216}$

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