The first challenge is to acknowledge that you can't absorb everything you think you need to know. Once you master that mental obstacle, things get easier.
You will be able to prioritize, delegate and just let things slide. You don't have to answer or even read everything that comes your way.
The idea of eliminating information is barely thinks. But this is about self-preservation.
Second, as you limit content, you'll learn to savor it more. Be ruthless as you can through all the "e-noise" and clear your decks for the important stuff.
Get started by spending sometime deciding what sources of information and intelligence are critical for you and your job. What are "must" reads?
Boil it all down to the highest-quality stuff, and read that first. Cancel or get rid of what's only marginal.
When you're the one doing the communicating, be more economical in everything you write, publish, broadcast and post online.
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