In a machine tool having at least one tool spindle which is displaceable in relation to a device for holding workpieces in at least one of three spatial directions and in which the tools (W1-W7) for processing the workpieces can be chucked, there are provided a machine magazine (36) in which tools (W1-W7) provided for exchange in the tool spindle (23) are kept in store and a background magazine (31) in which tools (W1-W7) provided for exchange in the machine magazine (36) are kept in store. In the machine magazine (36), not more than four storage places (42, 43, 44, 45) for accommodating tools (W1-W7) are provided (FIG. 2).

A tooling assembly for a machine having an automatic tool changing system includes a tool body disposed about a rotational axis and defining an internal passage operable to flow a fluid therein. The internal passage includes an inlet, stem channel, first and second curved channels, and first and second transition portions. The inlet is configured to receive the fluid from the machine. First and second outlets are open through an exterior of the tool body. The stem channel is in fluid communication with the inlet and ends at a beginning of the first and second transition portions. The first curved channel extends from the first transition portion to the first outlet. The second curved channel extends from the second transition portion to the second outlet.