Consider the following inequalities:
\[
p^2 - 4q < 4, 3p + 2q < 6
\]
where \(p\) and \(q\) are positive integers.
The value of \((p+q)\) is \underline{\hspace{1cm}}.
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In inequality problems with integer constraints, test small integer values systematically. Often only one pair satisfies both conditions.