responsibly
In a careful, trustworthy way that respects duties and others.
To act responsibly means to handle your duties and choices with care, thinking about how your actions affect yourself and others. When you act responsibly, you do what you're supposed to do without needing constant reminders, and you consider the consequences before you act.
A responsible student finishes homework on time, even when friends are playing outside. A responsible pet owner remembers to feed and walk their dog every day. A responsible friend keeps promises and shows up when they say they will. The word connects to responsibility, which means the duties or tasks you're expected to handle.
Acting responsibly means choosing the harder right thing over the easier wrong thing. It might mean admitting a mistake you made instead of blaming someone else, or saving your allowance for something important instead of spending it all immediately. When a teacher lets students work independently, she's trusting them to act responsibly by staying on task without supervision.
People earn trust by acting responsibly over time. When you consistently make good choices and follow through on commitments, others learn they can count on you. The opposite, acting irresponsibly, means being careless or ignoring your duties, which erodes that trust quickly.