Step 1: Evaluate the reason first.
The nitro group ($-NO_2$) is indeed a strong electron-withdrawing group, exerting both $-I$ (inductive) and $-M$ (mesomeric) effects. At the para position it efficiently withdraws electron density from the oxygen of the phenoxide ion through the ring, dispersing the negative charge and stabilising it. The reason is true.
Step 2: Determine the effect on acidity.
A more stable conjugate base (p-nitrophenoxide ion) means the equilibrium for proton donation lies further to the right. Therefore, p-nitrophenol is a stronger acid than phenol, not a weaker one.
Step 3: Evaluate the assertion.
The assertion claims p-nitrophenol is less acidic than phenol. Since p-nitrophenol is actually more acidic (its $K_a$ is larger), the assertion is false.
Step 4: Conclusion.
Assertion is false; Reason is true and correctly explains the stabilisation of the phenoxide ion.
\[ \boxed{\text{A is false, R is true}} \]