Modify a Turing Machine

How can we show that every Turing machine TM can be altered to a new  turing machine TM' which can perform 2 of 3 operations in every step, how can we define this altered turing machine.

TM: δ(Q x Γ) -> Q x Γ  x {L,R} 

TM':δ(Q x Γ) -> (Q x Γ) U (Γ x {L,R}) U (Q x {L,R})

Operations :

- move head (L or R ) and change a state, or write on tape and move head ,or write on tape
and change a state

Author: Alex Louis
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