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The reaction force is not infinite; it is finite. For example, if you push with a force of 100N, the wall will push back with a force of 100N.

If you are thinking that this requires an unlimited amount of energy, then you are confusing the concepts of force and energy. Energy is only required if the force is applied over a certain distance - the energy (or work) required to pull or push an object is equal to the force multiplied by the distance. In the example you give, the wall doesn't budge, so you have a force of 100 N times a distance of zero meters, equals an energy of 0 Joule.

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Q: I push a wall and it pushes back as long as I do - where does this infinite reaction force comes from?
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