Normally you simply insert a Button or Click Box object on slides. The default nature of these objects is to pause playback of the movie until the user clicks them.
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Thanks for answering my question so quickly, Rick. My problem seems to be solved. I'll explain my process here for anyone who might find it helpful in understanding button properties better.
I have an image button, chosen from the Cp button folder, set on Continue, and in options it's set to display for Rest of slide and to Pause after 2.9 seconds. The slide properties are set to display for 3 seconds. That slide works just like you say it should.
The next slide has the next button set to display for Rest of Slide and the Pause After box is unchecked. All other button properties are the same as the first slide's Next button. The slide properties are set at 300 seconds (I set it at this high rate as a workaround to make the slide appear as if it weren't advancing automatically). When you hit the Next button, this slide advances only after 300 seconds are up.
After that slide -- the next slide's Next button properties are Display for Rest of Slide with the Pause After box unchecked; On success is set on Go to Next Slide. Clicking on that button takes you to the next slide with no delay. HOWEVER, if you don't click the Next button at all the slide advances on its own. I got it to stop advancing automatically by checking the Pause After button. This action makes the slide pause until the user clicks the next button.
I love a mystery, especially when it's solved. Thanks again!