Evaluate: \[\lim_{m\to\infty}\left(\left(\sum_{n=1}^{m}\frac{1}{n}\sum_{k=1}^{n-1}\frac{(-1)^k}{k}\right)+\log(2)H_m\right)\]

The answer is of the form: \(\frac { { \pi }^{ A } }{ B } -\frac { { \left( \log { C } \right) }^{ D } }{ C } \) for positive integers \(A,B,C,D\).

Find \(A+B+C+D\).

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