Feel a little pull coming through on you

Two identical cylinders of mass \(m\) and radius \(r\) lie on a smooth horizontal table with a massless string wrapped around them as shown below. There is sufficient friction between the string and each cylinder such the string does not slip on them. The far end of the string is tied to a particle of mass \(m\). If one end of the string is pulled with force \(F\), the resultant acceleration of the particle is given by \(a=\Gamma \frac{F}{m}.\)

Find the value of \(\Gamma.\)

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