Reach 100

Dan and Sam play a game in which the first to start says the number 1, the next says 2, and the one who's next must say an integer strictly between the previous number and twice of it (not including the endpoints).

For example, Dan begins saying 1, then Sam says 2. Dan's options are now all integers between 2 and 4, exclusive. But there's only one such option, 3, so Dan is forced to say 3. Sam's options are now between 3 and 6, which are 4 and 5.

The game finishes when someone says 100 or greater; that player wins.

If Dan begins, who will win, assuming both players play optimally?

This is the first problem of the set Winning Strategies.

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