Designated Pilot Examiner reported a near miss in the traffic pattern when Tower Controller's instructions placed the reporter's aircraft on a converging flight path with another aircraft. Reporter conducted a go-around to avoid a collision.

Narrative

Incident at ZZZ airport on Day 0; near miss. Upon full stop landing on Runway XX ILS at ZZZ airport; we requested to taxi to the active runway which was Runway XYR. We were then given taxi instructions to XYR for a normal takeoff to be followed with a short field landing; full stop then taxi back to the FBO.On receiving takeoff clearance on XYR with tower advising us to make right traffic. On right downwind tower than advised us to extended downwind. Approx. 2/3 miles we were then instructed by tower to turn base (right base). On right base the Garmin 430m advised us; in yellow with voice warning; that we had traffic 100'ft below us; almost right on top of him. I immediately looked in front and to my left looking for traffic. Finally I say him at my 11 o'clock converging on me and saw he was around approx 300' ft horizontally; same altitude. I immediately took evasive action; going around and advise tower. A few seconds later I asked tower on why he had us turn right base. Tower replied ' I thought there was adequate spacing. Tower then said ' turn right' when I was already taking action and told tower we were turning right and climbing to avoid a near miss. Going around flying the upwind he later advised me I was 'cleared to land'. I repeated again that I was on the go-around and requested further instructions. He then said enter right traffic. Upon landing asked on ground XXX.XX for tower phone number that I wanted to talk to them about the incident/near miss. I spoke with Person A who was the acting manager at ZZZ tower and said they were reviewing the tapes at this time. Later ZZZ manager and supervisor called me an explained that he was advised of the incident and would get back to me after reviewing the tower tapes.Making my assessment of the incident; I think tower was overloaded with multiple aircraft doing takeoffs and landings; beautiful VFR day; with parallel runways in use. Maybe don't put so many aircraft in the pattern.