# Using multiple deciders in a Turing machine

I want to construct a Turing machine that compares two different decidable Languages in some way (e.g. $$L_a$$ and $$L_b$$). Suppose we have the deciders $$M_a$$ and $$M_b$$ for these languages.

Am I allowed to use both these deciders in the design my Turing machine $$M$$? By that I mean can I do the following on some input $$x$$ for $$M$$:

1. Input $$x$$ to $$M_a$$. If $$M_a$$ accepts go to step $$2$$. If $$M_a$$ rejects go to step $$3$$.
2. Input $$x$$ to $$M_b$$. If $$M_b$$ accepts, then $$M$$ accepts input $$x$$. Else, $$M$$ rejects $$x$$.
3. Input $$x$$ to $$M_b$$. If $$M_b$$ accepts, then $$M$$ rejects input $$x$$. Else, $$M$$ accepts $$x$$.

The idea behind this is that $$M$$ only accepts a string $$x$$ if $$M_a$$ and $$M_b$$ both accept or both reject it as well.

So is this not valid? Do I have to write the outputs of $$M_a$$ and $$M_b$$ to other tapes and compare those values instead?