We speak of boredom when arousal outweighs the challenges of a situation. You feel capable of doing more than your current surroundings demand from you. To overcome this imbalance you can either search for new stimuli or lower your level of arousal. Since being aroused is associated with the release of adrenalin and it is known fact that constant low doses of the stress hormone cause serious health problems, a minimalist approach to boredom seems a wise option.
There are various ways of dealing with boring situations that do not rely on external sources to draw your attention towards them. When you are occupied with a certain activity, it helps to entirely focus on that task, even if it seems trivial. If it is meaningful to you then so much the better, just reaffirm yourself with why you do it and what the benefits are.
Another reason why trying to escape boredom immediately is a bad idea is that over time you adapt to a certain level of stimulus and begin to feel bored a fortiori. The only way to get out of this spiral is to do something that you find meaningful, not just arousing. Thus, minimalism does not only help you to avoid sensory overload, but leads to solutions for more profound shortcomings.
You will find that by consciously exposing yourself to boredom you will not only be able to determine much more accurately what to do about it, but also have more energy in non-boring situations. Randomly completing tasks is like burning fuel with one foot on the brakes. In contrast, mindfully dealing with such situations empowers you to not just act out of psychological strain. Then your endeavors become an expression of true motivation.