Let \( n \) be a set of integers. \( S(n) \) is defined as the sum of the elements of \( n \). Consider the set \( T = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \). Let \( A \) and \( B \) be subsets of \( T \) such that \( A \cup B = T \) and \( A \cap B = \varnothing \). The probability that \( S(A) \geq 4S(B) \) can be expressed as \( \frac{p}{q} \). Compute \( p + q \).

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