
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
With four standard six-sided dice in play, Vivian rolls all four and can choose to reroll any subset of them. To win, Vivian needs the sum of the four dice after possibly rerolling some of them to be exactly 12. Vivian plays optimally to maximize her chances of winning. What is the probability that she chooses to reroll exactly three of the dice?
**A)** $\frac{1}{72}$
**B)** $\frac{1}{12}$
**C)** $\frac{1}{10}$
**D)** $\frac{1}{8}$
**E)** $\frac{1}{6}$

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