The rodent control task force went into the woods one day and caught $200$ rabbits and $18$ squirrels. The next day, they caught $3$ fewer rabbits and $2$ more squirrels than the day before. This pattern continued, with them catching $3$ fewer rabbits and $2$ more squirrels each day. Determine the total number of rabbits caught by the day when they caught more squirrels than rabbits.

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