
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
Amy rolls three fair six-sided dice. Then she checks the rolls and chooses to reroll any number of them, aiming to get a new total sum greater than 12 to win a game. What is the probability that she chooses to reroll exactly two dice to maximize her winning chances?
A) $\frac{7}{72}$
B) $\frac{1}{24}$
C) $\frac{5}{72}$
D) $\frac{17}{72}$
E) $\frac{15}{216}$

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