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Thermalization processes degrade the states of any working medium, turning any initial state into a passive state from which no work can be extracted. Recently, it has been shown that this degradation can be avoided if two identical thermalization processes take place in coherently controlled order, in a scenario known as the quantum SWITCH. In some situations, control over the order even enables work extraction when the medium was initially in a passive state. This activation phenomenon, however, is subject to a limitation: to extract non-zero work, the initial temperature of the medium should be less than half of the temperature of the reservoirs. Here we analyze this limitation, showing that it still holds true even when the medium interacts with $N\ge 2$ reservoirs in a coherently-controlled order. Then, we show that the limitation can be lifted when the medium and the control systems are initially correlated. In particular, when the medium and control are entangled, work extraction becomes possible for every initial value of the local temperature of the medium.