Taiga is our project management platform for monitoring of tasks except translation projects.
We usually use Kanban - a board where you can see and update the tasks, which belong to one desk.
There are several desks and you may be added to some of them and be responsible for the whole desk, for a task of for a subtask.
You should update the status of the task at least once a week even if nothing happening and let the Senior PM know if there any difficulties or questions.