Simple loop on file read and exit

I have a list of files I saved in a text file.  I want to loop through the list for each file and look in three specific directories for it.  I have that part working, except if the file in my list doesn't exist in any of the three directories, I want to skip that file in the list and move on to the next.  This is the part that I am having trouble getting to work.  If anyone can help, I would appreciate it.  I want to run this script on several unix systems.  Not all systems are the same.  Some have files that others do not which is why I have the complete list in a text file so that I can see what files are missing from that specific system.  Make sense?

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for FILE in `cat filelist.txt`
    do
      if test -f /directory1/$FILE
      then
          FILE="/directory1/$FILE"
 
      elif test -f /directory2/$FILE
      then
          FILE="/directory2/$FILE"
 
      elif test -f /directory3/$FILE
      then
          FILE="/diretory3/$FILE"
 
      else next FILE
    fi
 
  done