12. (5 points) Person A and Person B start working on the same day. The company stipulates: A works for 3 days and then rests for 1 day, B works for 7 days and then rests for 3 consecutive days. In the first 1000 days, the number of days on which A and B rest on the same day is $\qquad$ days.
【Analysis】Jia's rest days are multiples of 4, i.e., $4,8,12, \cdots 1000$; Yi's rest days are: $8,9,10$,
$18,19,20, \cdots$, so Jia only needs to rest on days that are multiples of 4,
every three numbers include one multiple of 4, which means that Yi will have 1 day overlapping with Xi Yangyang's rest day every 10 days worked, so with a cycle of 10, there are $1000 \div 10=100$ cycles,

each cycle has one day of overlap, so 100 cycles have a total of 100 days of overlap.
【Solution】Solution: Jia's rest days are multiples of 4, i.e., $4,8,12, \cdots 1000$;
Yi's rest days are: $8,9,10,18,19,20, \cdots$, so Yi only needs to rest on days that are multiples of 4,
every three numbers include one multiple of 4, which means that Yi will have 1 day overlapping with Xi Yangyang's rest day every 10 days worked, so with a cycle of 10, there are $1000 \div 10=100$ cycles,

each cycle has one day of overlap, so 100 cycles have a total of 100 days of overlap.
Therefore, the answer is: 100.