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. After rerolling, he wins if and only if the sum of the numbers face up on the three dice is exactly \(7\). Jason always plays to optimize his chances of winning. What is the probability that he chooses to reroll exactly two of the dice? Express your answer in the form \(\frac{k}{m}\), where the fraction is in simplest form. Please give the value of \(k + m\).

Let's think step by step and output the final answer within \boxed{}.
user