So yesterday i was taxiing out from the tarmac and backtaxied the runway, before i taxied i leaned the mixture, gave it a little throttle and got onto the runway, i needed a little more power to get the airplane moving so i gave it more throttle, well i must have had it leaned to much because the engine coughed so i enrichened the mixture and the rpms went up and i pulled the throttle back and taxiied normally. Question was i obviously had the mixture too lean, so from now on i will lean it less than what i had it at, did i do damage to the engine by having it leaned out to where the engine coughed when i gave it enough throttle? It was leaned like this for maybe 30-45 seconds or so before i had to enrichen to keep the engine from not dying on the throttle input. I have read that lean of peak can be bad, and i just wonder if that pertains to this. Thank you!