I would ask my colleagues or managers assigning the tasks when the deadlines for each task is? I would the prioritize the tasks in relation to my core job, those from my manager comes first, then non-core roles in order of the 1st strategy. In case of conflicts with timing, I'd set up a quick meeting with the colleagues involved together and to help resolve the matter. Then share the list of prioritized task with all colleagues involved, and ensure I communicate progress daily plus any issues that arise. Communication is key.