Undecidability: writing a symbol on Turing Machine's tape I wonder to know if given a Machine $M$, a string $x$ and a symbol $\phi$, would $M$ ever write $\phi$ ?

My approach

Maybe i can show if the problem is undecidable by contradiction using $M$ to prove $\operatorname{HALTING PROBLEM}$, but i'm stuck here. Any hints ?
First take a Arbitrary Turing Machine M and modify it so that on stopping state it will first write a new symbol $\phi$ that it won't write at any other time.

If you can decide that Machine M' will write that symbol then you can decide whether machine M halted.