Worship is conversation between God and those who are reconciled to Him through His Son. It is not an event but a relationship.
Evangelism happens because of two conversations: the one believers continue with God and the second one we start with someone who does not follow Christ.
Why do we then choose to make both actions, worship and evangelism so complicated?
God initiates both conversations and actually they are closely related.
We worship because God invited us to be a part of His plan.
We worship to bring glory to God.
We tell our story to others, as God's instrument, showing them how God wants them to be a part of His plan.
We tell others our story so that they too can glorify God through their worship.
John Piper in his book Let the Nations Be Glad! says it this way: "Missions is not the ultimate goal of the church. Worship is. Missions exists because God is ultimate, not man. When this age is over, and the countless millions of the redeemed fall on their faces before the throne of God, missions will be no more. It is a temporary necessity. But worship abides forever."
We are all called to worship and through our worship (during Sunday and from Sunday-to-Sunday) we are God's witnesses because of our worship. How we live is worship. How we live is witness. The witness conversation is an outflow of the worship conversation.