Ayase chooses three numbers $a, b, c$ independently and uniformly from the interval $[-1, 1]$.
The probability that $0 < a + b < a < a + b + c$ can be expressed in the form $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. What is $p + q$?


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