Step 1: Understanding the reaction.
The reaction involves the conversion of ammonia to a compound (A) using KOH and Br$_2$. This is indicative of the Hofmann bromamide reaction, where an amide (such as (A)) is treated with bromine and a strong base to yield an amine.
Step 2: Analyzing the second reaction.
The second step involves treating the product (A) with CHCl$_3$ and NaOH, which is indicative of the malonic ester synthesis or similar reactions to form a carboxylic acid. Here, the structure of (A) is likely to be an acetamide (CH$_3$CONH$_2$).
Step 3: Conclusion.
After the two reactions, the product X will be CH$_2$COOH, as it follows the structure of the carboxylic acid produced from the Hofmann and malonic ester-like reactions.