Step 1: Identify the reaction.
The reaction of amides with \( Br_2 \) and \( NaOH \) is called Hoffmann bromamide degradation reaction.
In this reaction, amides are converted into amines containing one carbon atom less than the parent amide.
Step 2: Analyze the Assertion.
Primary amides \( RCONH_2 \) give primary amines \( RNH_2 \) on treatment with \( Br_2/NaOH \).
However, secondary amides do not give secondary amines by Hoffmann bromamide reaction because they do not have the required \( -CONH_2 \) group.
Thus, the statement that primary and secondary amides yield primary and secondary amines respectively is incorrect.
Step 3: Understand stepping down of series.
In Hoffmann bromamide degradation, one carbon atom is lost from the parent amide.
For example:
\[
RCONH_2 \xrightarrow{Br_2/NaOH} RNH_2
\]
So, the reaction involves stepping down the series.
Step 4: Analyze the Reason.
The reaction involves migration of the alkyl or aryl group from the carbonyl carbon to the nitrogen atom.
During the reaction, the carbonyl carbon is removed as carbonate salt.
This explains the loss of one carbon atom in the product.
Step 5: Mechanistic explanation.
The amide first forms an N-bromoamide intermediate.
This rearranges through migration of \( R \)-group from carbonyl carbon to nitrogen, forming an isocyanate intermediate.
The isocyanate is then hydrolyzed to give the amine.
Step 6: Compare Assertion and Reason.
The Assertion is incorrect because secondary amides do not give secondary amines in this reaction.
The Reason is correct because it describes the migration and removal of carbonyl carbon as carbonate salt.
Step 7: Conclusion.
Therefore, the correct option is:
\[
\boxed{\text{Assertion is incorrect but Reason is correct}}
\]