Let $\vec{a}=\hat{i}-3 \hat{j}+7 k \hat{k}=2 \hat{i}-\hat{j}+k$ and $\vec{c}$ be a vector such that $(\vec{a}+2 \vec{b}) \times \vec{c}=3(\vec{c} \times \vec{a})$. If $\vec{a} \cdot \vec{c}=130$, then $\vec{b} \cdot \vec{c}$ is equal to
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