Transforming a general four-impulse to the center of mass frame

I’m currently stuck on a problem.
It’s about two particles colliding with each other, where particle $A$ is traveling in the positive $x$-direction and particle $B$ in the negative $y$-direction. The the total energy of each of the particles is given as $E_A=E_B=gamma M_0c^2=2M_0c^2$.

I arrived at the following total 4-impulse in the laboratory frame:
$$p_{Lab.}^{mu}=(frac{E_A+E_B}{c},p_A,-p_B,0)^intercal=(4M_0c,p_A,-p_B,0)^intercal$$

What I want to do now, is to find the 4-impulse in the center of mass frame of this problem, so $p_{CMF}^mu$, because I want to calculate the center of mass collision energy.

I thought about applying a rotation to $p_{Lab.}^mu$ in a way that the $y$-component vanishes and after that applying a Lorentz-Boost in the $x$-direction in a way that the $x$-component also vanishes.

I wanted to ask if this is the correct way to approach this kind of problem or if this is not correct and what other ways are there to do it. I would appreciate every answer, thanks!