About vector bundle-valued differential forms

Question

In my course I saw this question and I would like if it is posible. Let $$\pi:E\longrightarrow M$$ a finite dimensional complex vector bundle over a semi-Riemannian manifold $(M,g)$, with a hermitian structure $h$ and a compatible linear connection $$\nabla:\Gamma(M,E)\longrightarrow \Omega(M)\otimes_{C^\infty(M)}\Gamma(M,E)$$ (where $C^\infty(M)$ is the space of real-valued smooth functions). The question is if it is posible to define products $$\Omega(M,E)\times \Omega(M,E)\longrightarrow C^\infty(M)$$ $$\Omega(M,E)\times \Omega(M,E)\longrightarrow \mathbb{R} $$ where $\Omega(M,E)$ is the space of all $E$-valued differential forms on $M$. I suppose that the last one has to be a kind of inner product, but I am not so sure.