Step 1: Reaction with \( \text{NaOH} \).
The first step involves the phenol reacting with sodium hydroxide, which converts the phenol group into a phenoxide ion (P).
Step 2: Reaction with \( \text{CO}_2 \).
The phenoxide ion then reacts with carbon dioxide under basic conditions, resulting in the formation of a carboxylate anion (Q), which then undergoes protonation in acidic conditions to form a carboxylic acid group (R).
Step 3: Conclusion.
Thus, compound \( (R) \) is a carboxylic acid, \( \text{COOH} \).
Final Answer:
\[
\boxed{\text{COOH}}
\]