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I would like to talk about situation. When I was an engineering  manager at digital commerce platform org at Amazon, I was handling close to 11 services, and 

as part of the Rolling Stone initiative where Amazon was trying to move all its services away from Oracle, I had four services that I was trying to migrate from Oracle to the databases hosted on Azure. All my fellow colleagues who were owning services of DCP were doing similar exercise. One of the colleague who was owning digital redemption service had to go on maternity leave, and then couple of engineers earmarked to do this migration for digital redemption service wwere transition out of the organization. That is when I offered to help with the migration of the service. 

So I now had 5 services with competing  priorities where I 

had to manage very tight schedule of service migrations. Planning a very ruthless prioritization, figuring out an optimal execution path of a completely unknown service, interacting with the service upstream clients whom i had not worked with prior, working with an amalgam of My team members and the service owner team members were few of the ambiguous paths I navigated to help do on time migration completion of the   service owned by my collegues.

I was working with 5 customers at once, and had to focus on those activities where I could make a difference, make the most impact, that I could not delegate, and where I could balance with other priorities - in order to do that, I measured the priority of the tasks by the cost of delay, in other words, the impact of not doing them at that time. Then, with more clarity about the priorities, I thought which ones I could delegate to other team members, and if that made sense, with the required support and guidance from my side. Working as a team and not trying to get everything done yourself is key in the long term with multiple, competing priorities. Then, organizing my time well in short, focused timeslots for the most important tasks, made a difference.