Are laravel queues the right tool?

I am working on a tool that users upload files, the files are passed to an llm for transcribing and summarizing, then when the process is done it alerts the user that the transcript and summary are available to download. I can only have one llm process running at a time so what I would like to to is upload the file, fire off a queued job that calls the llm, wait for the llm to complete, log the output, then fire off an email to the user. Once that job ends the next queued job starts. Unfortunately the job can take 5minutes or longer in the test environment. Are laravel queues what I should be using or am I hammering a square peg into a round hole?