If $\vec{a},\vec{b}and\vec{c}$ are three non-zero vectors, no two of which ar collinear, $\vec{a}+2\vec{b}$ is collinear with $\vec{c}$ and $\vec{b}+3\vec{c}$ is collinear with $\vec{a},$ then find the value of $\left|\vec{a}+2\vec{b}+6\vec{c}\right|\dot{}$

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