Given that:-

\(a_1+a_2+a_3+a_4=1\)

\(a_1^2+a_2^2+a_3^2+a_4^2=2\)

\(a_1^3+a_2^3+a_3^3+a_4^3=3\)

\(a_1^4+a_2^4+a_3^4+a_4^4=4\);

The value of \(a_1^5+a_2^5+a_3^5+a_4^5\) can be expressed as the rational number \(\frac{p}{q}\), where \(p\) and \(q\) are mutually prime positive integers. Determine \(p+q\).

\(a_{m}^{n}\) is the \(n^{th}\) power of the number \(a_m\)

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