[Python] How to find the closest smaller value in a large sorted array efficiently

For a sorted list, how can I find the smallest number which close to the a given number?

For example,

mysortedList = [37, 72, 235, 645, 715, 767, 847, 905, 908, 960]


How can I find the largest element which is less or equal to 700 quickly? (If I have 10 million elements, then it will be slow to search linearly). In this example, the answer is 645.

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