Concept:
Marriage systems in sociology are classified based on rules regarding marriage within or outside social groups.
Step 1:
Endogamy means marriage within one's own social group, caste, tribe, or community.
Step 2:
The assertion is incorrect because endogamy does not specifically require marriage with first cousins only.
\[
A \text{ is incorrect}
\]
Step 3:
Exogamy means marriage outside one's own social group or category.
\[
R \text{ is correct}
\]
Step 4:
Since Assertion is false and Reason is true, the correct option must indicate this relationship.
Step 5:
Therefore, the correct answer is:
\[
\text{(A) is not correct but (R) is correct}
\]
\[
\boxed{\text{(4) (A) is not correct but (R) is correct}}
\]