This is unfortunately not trivial, but here are a few ways to do it:
A) Create a master action sequence that marches through all the states:
1. Put your states inside a custom component. If you haven't used Custom Components before, just select some artwork and choose "Convert to Component > Custom Component". Then double-click the component and start adding states.
2. Outside the custom component (in the main application), create a button. This will be used to start the animation.
3. In the Interactions panel, add an interaction: On Click > Play Action Sequence. When you choose OK, Catalyst will show the action sequence in the Timelines panel.
4. Select the custom component. In the Timelines panel, choose "Add Action > Set Component State". In the Properties panel, choose the first state.
5. Repeat step 4, choosing each subsequent state.
6. Space out these "Set component state" interactions on the timeline.
B) This is a total hack that I just discovered, but it works. You can use a video component to automatically go to the next state after going to one state.
1. First, you'll need any FLV video. You should just use an empty one.
2. Go to one of the states that should just continue to the next state.
3. Import the FLV file "File > Import > Video/Sound File".
C) If you're willing to write some code, you can import your project to Flash Builder and write a handler for the "currentStateChange" event.