Why is the product of the reaction between iron and steam is iron (II, III) oxide and not iron (II) oxide or iron (III) oxide? The reaction between Iron and steam in my textbook is given as this:

$$\ce{3Fe + 4H_2O &lt;=&gt; Fe_3O4 + H_2} $$

My question is why these following reactions are not possible or do not happen.
$$\ce{Fe + H_2O &lt;=&gt; FeO + H2}$$ 
$$\ce{2Fe + 3H_2O &lt;=&gt; Fe_2O_3 + 3H2}$$

I mean, how do the atoms know to form iron (II,III) oxide instead of Iron (II) oxide or iron (III) oxide in this reaction?
Recall that $\ce{Fe3O4}$ is basically just an equimolar mixture of $\ce{FeO}$ and $\ce{Fe2O3}$. So, in that way, both of the reactions that you mentioned do infact happen, and the result is what was mentioned in your textbook.