A Golden Fraction II

\[0.1123101\ldots\]

Consider a decimal such that the \(n^{\text{th}}\) digit to the right of the decimal place is the \(n^{\text{th}}\) term of the Fibonacci Sequence \(\mod 4\), as shown above.

The exact value of this decimal can be expressed in the form \(\dfrac{a}{b}\) for coprime positive integers \(a\) and \(b\).

What is the value of \(a+b\)?

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