How many ordered pairs of integers \((a,b)\) satisfy all of the following inequalities? 

\[ \begin{align*} 
& a^2 + b^2 < 16 \\
& a^2 + b^2 < 8a \\
& a^2 + b^2 < 8b 
\end{align*} \]

Let's think step by step and output the final answer within \boxed{}.
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