The student pilot had landed the aircraft and was in the process of taking off for another circuit. The instructor stated, “Full power, right rudder, I’ll do the flap”. The student followed the instructions and the aircraft veered right, off the runway. The aircraft wheels instantly dug into the very soft muddy ground at the side of the runway, bringing the aircraft to a sudden stop. As a result the nose landing gear collapsed and the propeller struck the ground. The instructor concluded after the incident that the student had applied excessive rudder and held it. The aircraft had reacted too quickly for the instructor to intervene and correct the rudder pedal input before the aircraft left the narrow runway.