The problem

Source : MS Couhan (problems in organic chemistry . Chapter: Alcohols , phenols and ethers).

My Thoughts

If I proceed along $\ce{path 1}$ , $\ce1a$ is formed . It is unstable due to inductive withdrawing effect of $\ce{C=O}$ neighboring to it. Eventually $\ce2$ is obtained.

However, along $\ce{path 2}$ relatively more stable $\ce{3a}$ (compared to $\ce{1a}$) is formed. $\ce3a$ on ring expansion gives $\ce{3b}$ , leading to $\ce{4}$ ($\ce{3b}$ is relatively unstable compared to $\ce{1b}$).

My question

Which of the two paths should I choose that would lead to a major product ?