Reversed Branched logs

Algebra Level 4

\[\begin{cases} \log_3(\log_2x)+\log_{\frac{1}{3}}(\log_{\frac{1}{2}}y)=1 \\ xy^2=4 \end{cases} \] If the above equations hold for some values of \(x\) and \(y\), then find the value of \(xy\).


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