What should I use here - Need changing value in different processes

You picture is too small to see the signal names.

R will get set high as soon as run_i goes high. It wont go low again until done is '1'.

and I just noticed that the ACTION process uses the stepper clock in the sensitivity list, but it is NOT a clocked process. So therefore its all wrong. You need to remove stepper_clk_i from the sensitivity list and add count, D, derection_cntrl, R, halt_cntrl, speed+cntrol, H. THis process will also create latches, as you have incomplete if statements.

ACTION : process(R, D, H, count,derection_cntrl, halt_cntrl, speed_cntrl)

Plus, putting adders in asynchronous processes is a bad idea.