Relativity: Energy and Momentum

A particle with rest mass $m$ is in a particle accelerator and is at rest in the accelerator's reference frame. Another particle with rest mass $m$ is driven into the first particle with a speed of $\frac{4}{5}c$ with respect to the accelerator. The two particles undergo a perfectly inelastic collision with no dissipation of energy.

Compute the speed of the new particle in the accelerator's reference frame.