Fortran OMP : how to do a parallel and a single task?

Question

I am a newbie in parallel programming. This is my serial code that I would like do parallelize

program main
  implicit none
  integer :: pr_number, i, pr_sum
  real :: pr_av
  
  pr_sum = 0
  do i=1,1000
! The following instruction is an example to simplify the problem.
! In the real case, it takes a long time that is more or less the same for all threads
! and it returns a large array
   pr_number = int(rand()*10) 
   pr_sum = pr_sum+pr_number
   pr_av = (1.d0*pr_sum) / i
   print *,i,pr_av ! In real case, writing a huge amount of data on one file
 enddo

 end program main

I woud like to parallelize pr_number = int(rand()*10) and to have only one print each num_threads. I tried many things but it does not work. For example,

program main
  implicit none
  integer :: pr_number, i, pr_sum
  real :: pr_av
  
  pr_sum = 0
!$OMP PARALLEL DEFAULT(SHARED) PRIVATE(pr_number) SHARED(pr_sum,pr_av)
!$OMP DO REDUCTION(+:pr_sum)
  do i=1,1000
   pr_number = int(rand()*10)
   pr_sum = pr_sum+pr_number
!$OMP SINGLE
   pr_av = (1.d0*pr_sum) / i
   print *,i,pr_av
!$OMP END SINGLE
 enddo
!$OMP END DO
!$OMP END PARALLEL

end program main

I have an error message at compilation time : work-sharing region may not be closely nested inside of work-sharing, critical or explicit task region.

How can I have an output like that (if I have 4 threads for example) ?

       4   3.00000000    
       8   3.12500000    
      12   4.00000000    
      16   3.81250000    
      20   3.50000000  
      ...

I repeat, I am a beginner on parallel programming. I read many things on stackoverflow but, I think, I have not yet the skill to understand. I work on it, but ...

Edit 1

To explain as suggested in comments. A do loop performs N times a lengthy calculation (N markov chain montecarlo) and the average of all calculations is written to a file at each iteration. The previous average is deleted, only the last one is kept, so process can be followed. I would like to parallelise this calculation over 4 threads. This is what I imagine to do but perhaps, it is not the best idea.

Thanks for help.