Reaction mechanism of rearrangement I am currently studying for my organic chemistry exam, but there is one problem I do not understand. Unfortunately, I do not have any solutions.

See image for the problem.



My first thought was the Dienone-phenol-rearrangement. But in order to do so, I need to add the alkyl substituent and I need a dienone. So can I deprotonate the phenol using potassium carbonate? (Or is it too weak as a base? The pKa of bicarbonate is around 10, so maybe it is too weak) But if it is possible, then the free electron pair of the oxygen can form a ketone... I could then use the alkene with a chloride substituent, so that the aromatic ring can attack it. Then I would have the dienone. But with the Dienone-phenol-rearrangement, the alkyl substituent can only move by one carbon-atom in the ring...

Is my thought process wrong? Can you please help me?

I did not have any lectures on rearrangement reactions, I had to learn them by myself, but by now, I have not found any similar reactions.

Thank you!
The first reaction is O-alkylation of p-cresol to give a 4-methylphenyl allyl ether derivative 3. The reagent in the first box should be 1-bromo-3-methylbut-2-ene (1; see the top box in the picture), which would undergo $\mathrm{S_N2}$ reaction with phenolic anion (2) in refluxing acetone. Note that potassium carbonate is a strong enough base to complete this reaction (this is surely a strong base than potassium bicarbonate). 



The product 3 from alkylation would undergo Claisen rearrangement upon heating to give final alkylated cresol 4 in solvent-free condition. Remember, Claisen found his famous rearrangement first in solvent-free conditions, while he was trying to find the melting point of newly synthesized naphthyl allyl ether! (Picture is from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3873100/ and modified accordingly)