The [i]Purple Comet! Math Meet[/i] runs from April 27 through May 3, so the sum of the calendar dates for these seven days is $27 + 28 + 29 + 30 + 1 + 2 + 3 = 120.$ What is the largest sum of the calendar dates for seven consecutive Fridays occurring at any time in any year?

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