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Edited
There are no privileged frames of reference.
The action is Lyra’s hoo…hand pushing on Luna’s chair. The reaction is Luna’s chair pushing on Lyra’s hoo… hand. Hand. Lyra’s hand.
Or the action is Luna’s chair’s mass resisting Lyra’s hand, and the reaction is Lyra being imparted with opposite momentum to Luna.
Or…
The action is Lyra pushing Luna.
The equal reaction is Luna moving off in that direction.
The opposite reaction is Lyra moving off in the other direction.