Can't speak for the 777 but on our 756 fleet our reject procedure is :
Throttles-idle, disconnect autothrottles (activates RTO maximum available braking above 80 knots)
Reverse-to interlock then full reverse (interlock will deploy all available spoilers)
This sequence of actions provides for the most rapid application in the most efficient sequence of all deceleration devices.
If, of course on pulling the throttles to idle RTO brakes do not engage (and this is a required call out for us) then manual braking must be used, you are far better off, however letting the RTO function provide RELENTLESS maximum braking to a stop while you keep it straight.
Similarly if deploying reverse does not activate spoilers you can rapidly pull the lever yourself.
Stick with the automatics for max stopping and override if one or more does not function.
