Our righteousness is what Christ did for us AND what we let Him do through us. We were justified (right-wised) by faith and not law. Justified, in the NT, means that we were set in right relationship to our Father and set on a course of righteousness (right action). Doing righteousness are the actions of obedience, compassion, mercy and justice done in covenant with God. The driving force behind acts of righteousness is love. It is by love that we seek the good of our fellow humans. The righteous do these righteous things because the love of God in their hearts is spilling out through them, i.e., humans acting in synergy with God. It is working out what God works within (Philippians 2:12-13). It is such perfect synergy that you can’t always divide human energy from God’s energy, because grace has blended them.
“By this it is evident who are the children of God, and who are the children of the devil: whoever does not practice righteousness is not of God, nor is the one who does not love his brother.” 1 John 3:10 (ESV)