Saving all random numbers generated by the program then reusing them in racket

I have a project making calls to random numbers, for example:

I have calls that look like this: (random) to generate numbers between 0 and 1, also calls like this: (random n), to generate numbers within range.

What I want to do is put all the random numbers generated throughout the program in a file.

I have this code:

  (require (rename-in racket [random random0]))

  (define random-port (open-output-file "random-numbers.rktl" #:exists 'replace))
  (define (random x)
    (define y (random0 x))
    (displayln y random-port)
    y)

But this isn't working for just (random), but rather for (random n). Is there anyway to make it work for both?

Secondly, where can I put this code if I have multiple modules using random?

Finally, for some reason, when I write something like this:

  (for ([i (in-range 100000)]) (random 10))

The numbers are displayed without a problem in the file,

but when I write this: (random 10), I'll get an empty file.

Any help will be really appreciated. Thank you!