Step 1: Phenol reacts with NaOH and CO$_2$ to form salicylic acid via Kolbe's reaction (X = salicylic acid).
Step 2: Salicylic acid reacts with acetic anhydride ((CH$_3$CO)$_2$O) in the presence of acid (H$^+$) to yield aspirin (Y).
This transformation involves acetylation of the hydroxyl group of salicylic acid, forming acetylsalicylic acid (aspirin), which corresponds to Option (2).