Steady on chaps, maybe what Ifrochao was asking is “Is assumed temp thrust reduction allowed with improved climb”.
My present company does not allow it but my previous one did. Personally I don’t see why you should not be allowed to do the two together. If you have excess runway and need to lift more weight then using improved climb will solve the problem. Fine, but why should you also have to do a full thrust take-off thereby increasing your chances of having an engine failure. If its stopping at V1 you are worried about then the numbers either say you can or can’t do it, there is no grey area. If you can’t then go full thrust, otherwise reduce your chances of having the V1 stop by using an assumed temp thrust reduction.
The two techniques are different and achieve different things, one gets you more take-off weight the other preserves engine life. If you can have both together then so much the better, it should be no problem on a very long runway but check your figures carefully.
This is the section on Assumed Temp from the FPPM (Page 1.1.4) for the 737-700. Note it does not prohibit use with improved climb. The section on Improved Climb was much longer so I didn’t paste it here, but it also makes no mention of not combining with an assumed temp:
Assumed Temperature Reduced Thrust
Regulations permit the use of up to 25% takeoff thrust reduction for operation with assumed temperature reduced thrust. Use of reduced thrust is not allowed on runways contaminated with standing water, ice, slush or snow. Guidance for setting reduced thrust is provided for the flight crew in the Performance Inflight Chapter of the QRH. Use of assumed temperature reduced thrust is not recommended if potential windshear conditions exist.
S & L