In the diagram, $$\(O A B\)$$ and $$\(O E D\)$$ are straight lines. O is the origin, $$\(A\)$$ is the midpoint of $$\(O B\)$$ and $$\(E\)$$ is the midpoint of $$\(A C\)$$. $$\(\overrightarrow{A C}=\mathbf{a}\)$$ and $$\(\overrightarrow{C B}=\mathbf{b}\)$$. Find, in terms of $$\(\mathbf{a}\)$$ and $$\(\mathbf{b}\)$$, in its simplest form $$\(\overrightarrow{A B}\)$$, $$\[ \overrightarrow{A B}= ............................................ \]$$

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