\[\large \sqrt{x+1}+\sqrt{3-x}+2\sqrt{(x+1)(3-x)}\leq m+1\] If there exist a range of \(m\) that makes the above inequality holds true for all \(x\), find the minimum value of \(m\) in that range.

Submit your answer to 2 decimal places

*Note: if you think there are no range exist or that range have the form \((\alpha;\beta\)); submit your answer as \(1.11\)

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