It is widely known that Kant's first formulation of the categorical imperative, in his Metaphysics of Ethics, is as shown:
Act only according to that maxim whereby you can at the same time will that it should become a universal law.
The question I have is whether performing an action to secure a win in competitions, such as crossing the finishing line in order to clinch the first place in a marathon, can be interpreted as a violation of the categorical imperative, and is therefore immoral. This is because universalizing the maxim of performing the said action (ie. run through the finishing line so as to get first place) to win in competitions will involve a contradiction since if everyone performs an action to secure the first place in competitions, then no one can possibly clinch the first place in any competition.
However, the conclusion that I have come about, namely performing an action to secure the first place in competitions is immoral, is absurd. In which part of the argument did I misinterpreted/misused Kant's categorical imperative? Sorry, I have just started learning the concept of categorical imperative, so I do not have a rigorous or deep knowledge of this concept.