ok so you are saying that when you reach thrust reduction altitude you will transition to climb power and the derate/reduced thrust story ends, right ?
here's what the 737 FCOM says about pushing TOGA,
"After LIFT-OFF:
• the A/T remains in THR HLD until 800 feet RA. A/T annunciation then
changes from THR HLD to ARM and reduction to climb thrust can be
made by pushing the N1 switch.
Note: During a reduced thrust takeoff, a second press of the TO/GA switch
below 800 feet RA will change the thrust limit mode to GA and N1
reference bugs to increase to full GA thrust, thrust levers will not be in
motion. A second press of the TO/GA switch above 800 feet RA, thrust
levers advance toward full GA thrust.
• automatic reduction to climb thrust occurs upon reaching the selected
thrust reduction altitude which is shown on the FMC CDU TAKEOFF
REF page 2/2 during preflight, or when the airplane levels off in ALT
HOLD or VNAV PTH. Pilot entries can be made to override the default
value. Allowable entries are 800 feet to 9999 feet
• flight director engaged status is terminated by engaging an autopilot in
CMD (CMD replaces FD in A/P status display)
• pitch engages in LVL CHG and pitch mode FMA is MCP SPD unless
another pitch mode has been selected
• MCP IAS/Mach display and airspeed cursor change to V2 + 20 knots
• roll mode engages in HDG SEL unless another roll mode has been
selected.
To terminate the takeoff mode below 400 feet RA, both F/D switches must be
turned OFF. Above 400 feet RA, selection of another pitch mode or engaging an
autopilot will terminate the takeoff mode; other F/D roll modes can be also
selected."