On a table, there are $10\,000$ matches, two of which are inside a box. Ana and Beto take turns playing the following game. On each turn, a player adds to the box a number of matches equal to a proper divisor of the current number of matches in the box. The game ends when, for the first time, there are more than $2024$ matches in the box and the person who played the last turn is the winner. If Ana starts the game, determine who has a winning strategy.