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Classic Sonic would play like he did in generations or Sonic 1-CD I think the timeline would take a detour from adventure and continue onto it's own timeline with it's own original games to boot the music would still be sonic like only more modernized (we don't want dying cats or ducks Sega) similar to how a fan game known as Sonic After the Sequel handled music.

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Boom is a unfortunate series and for multiple reasons mainly it's first two games and the average tv show and it's due to that the series is often considered bad but I did have two ideas here (the original being to polish the original gameplay style of Shattered Crystal and fix it's problems but I could already smell the flame pie and it's side of controversy maple) unless fire and ice make things better which it should (it was delayed how often does Sega delay a game?) I think It should play similar to adventure with some elements of...
[img=NaNxNaN]http://i.imgur.com/DoSbDkK.png[/img]
thrown in such as RC cars only, using the cars to allow you to upgrade certain things (similar to how they were utilized in runners) or the same effect as in lost world with the gameplay similar to adventure 1&2,no chao garden and if it is in there at least make it optional (no collectibles in the darn thing!)

 [img=NaNxNaN]http://i.imgur.com/vi7c8.png[/img]
Modern Sonic would play like he did in colors,generations,and unleashed (day) only I think it should have clever use of the boost,stomp,etc but maybe have a charge up for each (say for example spikes that are off center and pop out at nearly the same time and quickly but it's the only way down and the right is blocked off so naturally you use the stomp but out of nowhere... SUDDEN CONCRETE BLOCK and it lands you on the level of 2 sets of spikes! well you only have a few remaining seconds charge up that stomp move and before you know it the concrete block will disappear and you'll escape unscathed) or for another example lets say there's a pillar falling like in the 3DS version of sonic generations:
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but it has great reach to the point your normal boost speed can't outrun this one charge boost and you'll go much farther than a normal boost with one catch you use up all your boost energy and it reqiures a full boost gage for the full effect basically it's kinda similar to the special moves used in the dream snowboard event in Mario & Sonic at the Olympic winter games (ds) you press the button once normal boost but hold it
and you'll charge the boost. these are just examples though so if you have a better idea feel free to share it below!