Memory built-in self-test with automated multiple step reference trimming

A memory device can sense stored data during memory read operations using a reference trim, and a memory built-in self-test system can perform a multiple step process to set the reference trim for the memory device. The memory built-in self-test system can set a reference trim range that corresponds to a range of available reference trim values and then select one of the reference trim values in the reference trim range as the reference trim for the memory device. The memory built-in self-test system can set the reference trim range by prompting performance of the memory read operations using different positions of the reference trim range relative to read characteristics of the memory device and set a position for the reference trim range relative to the read characteristics of the memory device based on failures of the memory device to correctly sense the stored data during the memory read operations.