I tested with the following values, and the output voltage varied from 3.1V to 25.9V. The maximum that I need is 25V, so 25.9V is OK. The lowest output voltage is also OK.
R1=1.2K, R2=10K pot, R3=680R, R12=6K8 and R10=2K2.
There is a problem that still persists, the 10K pot has a "dead" portion on the low voltage. When the output voltage is abut 3.1V, the voltage starts to rise only when the pot is at about 1/4 of its course.