Consider the following random experiment: First, roll a die and observe the number of dots facing up; then, toss a coin the number of times that the die shows and observe the total number of heads. Thus, if the die shows three dots facing up and the coin (which is then tossed three times) comes up heads exactly twice, then the outcome of the experiment can be represented as (3, 2). Determine a sample space for this experiment. Determine the event that the total number of heads is even.

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