Slide with contact separate parts

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Hello
I'm trying to figure out, if it is possible in Inventor assembly slide one parts with move of two or more separate parts.
For example if I've two separate tiles, slides with Joint back and forth inside the box, which is also has separate shaft, slides vertically in own slot front of these two tiles.
Оne tile has "upward" slice, the other "downward" (cuts circled in green below).
If goal is to lift rod up, when "upward" extends and touches the rod and move it down when second moves forward:
The Tangent Constrain allows contact with inextricable link one part with single connection of move number of parts in single one.
The only solution I know is a Contact set, which physically behaves as required, moves one part when contacts with separate moving parts and breaks contact link, but doesn’t work accurately enough (like Slider Join or Tangent Constrain in its own way) if mechanism has a lot of parts.
Any guide, advice or example would be helpful