reciprocate

verbs

act, feel, or give mutually or in return
"We always invite the neighbors and they never reciprocate!"
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is a type of (narrower)
perform an action, or work out or perform (an action)
"think before you act"; "We must move quickly"; "The governor should act on the new energy bill"; "The nanny acted quickly by grabbing the toddler and covering him with a wet towel"
alternate the direction of motion of
"the engine reciprocates the propeller"
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is a type of (narrower)
move so as to change position, perform a nontranslational motion
"He moved his hand slightly to the right"