thevenin - Thévenin equivalent with a dependent source

I'm working in a circuit with some switches and it has the same configuration but different elements between ab. I am not sure if is possible to get a Thévenin equivalent of the next strange subicircuit to simplify calculations:

^{simulate this circuit – Schematic created using CircuitLab}

Answer

Since \$i_x \$ is not associated in any way with the output port AB, \$i_x\$ is an independent variable and thus, as seen from the port AB, the CCVS is an independent source. The Thevenin equivalent is:

^{simulate this circuit – Schematic created using CircuitLab}