This psalm moves from lament to praise.
There are no mentions of enemies in Psalm 77 and only a brief mention of troubles in vs. 2. However, his trials must have been intense for they lead him to question if God is who He revealed Himself to be. In vs. 7-9 what has happened to God's lovingkindness,  grace, and compassion. These are terms by which God reveals HImself in Exodus 34:6-7. The words of Exodus 34:6-7 are basically repeated in the Psalms in 86:5, 15; 103:8; 145:8. Is God who He said He was??

The exodus is the answer in vs. 11-20. The exodus is proof for all people of all time that God delivers those who trust HIm.