exert
To use a lot of effort, strength, or power.
To exert means to put forth effort or to use strength, power, or influence to make something happen. When you exert yourself while running up a steep hill, you're pushing your body hard. When a coach exerts her authority to settle an argument between teammates, she's using her position to create order.
The word captures that sense of deliberate effort or force being applied. A scientist might exert pressure on a sealed container to test its strength. A parent might exert influence over a school decision. You exert mental energy when concentrating hard on a difficult problem. Athletes exert physical power during competition.
Exertion is the noun form. After a day of heavy exertion, like helping a friend move furniture or playing several soccer games in a row, you feel tired because you've used up your energy. The amount of exertion required varies: solving a crossword puzzle requires mental exertion, while climbing a mountain demands serious physical exertion.
Notice that exerting yourself isn't the same as just being busy. Scrolling on a phone keeps you occupied but doesn't require much exertion. Real exertion means actively pushing yourself, applying force, or working to achieve something that takes genuine effort.