Which UPS with remote control should I choose?

Question

Uninterruptable power source

Good evening.
An interesting problem arose ...
There is a unit that is turned on and off with the "BIG RED BUTTON", there is a need to power the control logic of this unit through the UPS.
Those. there should be the following logic of operation:
1. Pressed BKK - the unit turned on, the UPS turned on => power went to the control part
2. Pressed BKK - the unit turned off, the UPS turned off => power was lost from the control part
3. Power was lost outside the unit, UPS works => control part works.
Those. in fact, I need to somehow control the on / off of the UPS with an external button.
The decision to put the UPS before the BKK (that is, so that it is always connected to the network) is not suitable, because. there is a requirement for a complete de-energization of the system when you press the BKK.

Answer 1

Indistinct formulation of the problem - indistinct and solution.
Every UPS has a Big Gray Button that turns the UPS on and off. Pull the wires from it to the BKK. Make the BKK paired - one pair of contacts controls the Unit, the second pair controls the UPS.