Step 1: Examine the assertion.
Accumulation of the desired product during fermentation can inhibit microbial growth or enzyme activity, thereby reducing the overall productivity of the process.
Hence,
\[
\boxed{\text{Assertion [A] is true}.}
\]
Step 2: Examine the reason.
Many accumulated products act as inhibitors by affecting enzyme function or decreasing cell viability.
Thus,
\[
\boxed{\text{Reason [R] is true}.}
\]
The reason correctly explains why product inhibition lowers process productivity.
Therefore,
\[
\boxed{(A)}
\]
is the correct answer.