A particle of mass 4.12 × 10-27 kg, moving at 4.62 × 105 m/s, strikes an identical particle which is initially at rest. After the interaction, the particles (which can't be distinguished) are observed moving at angles 55.3° and 34.7°, both angles being measured with respect to the original direction of motion. What are the final speeds of the particles? Please provide step-by-step method to get the answer.