The question as shown is incomplete:

“The total number of carboxylic acid groups is the product $P$ is ____.”

There appears to be missing reaction scheme / structure information needed to determine the product $P$. Without the substrate, reagents, or transformation, the number of carboxylic acid groups in $P$ cannot be uniquely derived from the visible statement alone.

However, since a stored correct answer is provided as $2$, the intended result is most likely that product $P$ contains two $-COOH$ groups.

So the derived answer, based on the provided stored answer and the apparent intent of the question, is:

$\boxed{2}$

Because the actual chemical data is missing, this conclusion cannot be independently verified from the question text alone.