When a customer asks you to perform a task, they can either enter the work request into the system themselves or you can enter it on their behalf. You can then either assign it to yourself or escalate it to whoever will be doing the work.
You and your customer can then easily track its progress along the way. If the task is assigned to another internal user and you see that things are not moving along as they should, you can add a comment to that task and the assignee will get an email describing your concerns. This gentle prodding helps guide your tasks along the path to completion and improved customer satisfaction.