is the best way to differentiate the type of reaction that should be used (electrocyclic, cycloaddition, or sigmatropic) when only given one reactant?...

In pericyclic reactions, what it is the best way to differentiate the type of reaction that should be used (electrocyclic, cycloaddition, or sigmatropic) when only given one reactant?  I am getting confused with what type of reaction to use and whether to open a cyclic molecule into a chain or close it into a ring.  I am specifically struggling with number 28. I have attached the questions in one image and the respective answers in another

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