Connecting individual road segments that participate in a dead end

I am trying to get a road feature class ready to do some analysis, regarding dead end roads. I have a road dataset cleaned up with continuous single segments, split at each road intersection. I have also added a field [DEADEND] noting any segment that dead ends (created through dangle topology). I have also identified any road segment that connect a dead end dangle with a non-dead end road (roads that have intersections on both ends). For example, a road that connects to multiple branching dead ends at one end and a non-dead end on the other, which would not be identified as a dangle in topology (as it has a vertex on each end, but is still part of a dead end).

If I query out the the segments ([DEADEND]="YES"), how do I merge the connected dead ends(sharing vertices) into individual continuous lines.

See picture for example.

I would like all segments labeled in green or purple into one line feature, without using the merge tool in the editor toolbar.