When you need to fine tune the animation timings, you need to display the very powerful Advanced Timeline. When you open the animation pane, which do you see:
With the advanced Timeline you can see the duration, start and end for each animation in relation to the other animations. For advanced animation needs the WITH PREVIOUS setting is utilized more and the animation start position and duration are adjusted with the Advanced Timeline (as example when a subtle overlapping animation is needed).
To see the Advanced Timeline, click any animation and choose SHOW ADVANCED TIMELINE.
There are some good examples of the advanced timeline in use on the Tutorials page.
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