How to make it so that AC power can be turned on by either side?

Question

Electronics

Sorry for the newbie question, but I can't seem to find a very popular circuit for sure.
I need to control an AC motor with a solid state relay. The relay has 2 contacts for alternating current (phase and working zero) and two for constant current (zero and phase). If I mix up the phase with zero, then the relay will die. I ask you to advise the scheme so that the plug can be inserted into the socket by either side, without fear for the performance of the device.

Answer 1

If the relay is for alternating current, then the phase and zero are not critical. Because relative to zero, the voltage goes both positive and negative. Just cling to the change, nothing will die from this.
But what they advise to put a bridge ... if there are thyristors / triacs inside, then it may lose the ability to close without crossing 0.
I didn’t understand the piece

two for constant (zero and phase)

What was it anyway? There are + and - on the constant. (It looks like we are talking about the control contacts of the relay?)

Answer 2

Sorry, very vague wording. Let's clarify.

I need to drive the engine

What do you mean by the term "manage" - only on-off or also change traction / speed? Or even reverse? A solid-state relay can do all this, but the circuitry in these cases is significantly different. What will be the governing body? A button, two buttons, a toggle switch, an electric signal (what?) or something else?

AC motor

There are a whole bunch of options: asynchronous or synchronous (with a phase shift using a capacitor or a short-circuit coil), collector-brush (many models work great at a break) - which one is yours? And what is the power, at least an order of magnitude?
UPD1. OK, let's continue.

asynchronous motor pump. It is required to turn on / off and change the rotation speed.

First, what is an asynchronous? With a capacitor? Secondly, the asynchronous speed is usually tied to the power frequency (a few percent slower than the synchronous frequency) and is practically not regulated. When you try to change the speed by adjusting the supply voltage, troubles begin: a sharp decrease in the torque on the shaft and its instability, an increase in losses (overheating). And how were the speeds regulated in the original version? Was it by chance that the frequency was adjusted? If yes, then it changes the whole approach.
UPD2.

speed control only during acceleration and deceleration

Well, then you can really use voltage, i.e. triac controller, the executive element of which is the same relay with an optocoupler input. When turned on, let it start from 40 ... 50%, and then rise to 100% in a couple of seconds. To do this, your controller software must include a 100Hz PWM routine.

I asked the question only in order to connect the pump not to the uninterruptible power supply, but directly to the outlet.

I don't understand what you are excited about. A triac relay is a thing symmetrical with respect to polarity (well, or at least it should be), nothing changes from the position of the plug in the socket in the relay. At the input - too, since it is galvanically isolated through an optocoupler. So there is no reason to panic.