Thévenin with dependent source and unknowns?
There are several ways to determine the Thévenin equivalent circuit of a given electrical diagram. In the present case, there is one fixed source and a voltage-controlled current source. According to a paper written by Mr. Leach, it is possible to apply the superposition theorem and alternatively turn sources on and off, even the controlled one. The trick, in this case, is to start by determining the control variable, \$V_1\$ in this exercise. Here we go:



Once the control variable is obtained, then you can apply superposition again to obtain the Thévenin voltage:



Then, to determine the Thévenin resistance, short the \$V_A\$ source and install a test generator across the output from which you want to determine \$R_{th}\$. This is exactly as what is described following the fast analytical techniques to determine time constants. Here, you can simplify the analysis because \$R_3\$ is in parallel with the intermediate result which itself is in series with \$R_2\$. The circuit to solve ends up being the simple below one:



Once this is done, a quick Mathcad sheet and a SPICE simulation tell you if this is good or not. In SPICE, a .TF (transfer function) calculates the output impedance at the considered node, directly giving the small-signal resistance \$R_{th}\$ you want:



Applying superposition to controlled sources represents a valid extension of the original theorem as this example shows.