<s>[INST] Let $F : \mathbb{Z} \to \mathbb{N}$ be a function with the property that $F(a) \leq F(a+b) \leq F(b)$ for any $a$, $b \geq 0$. Define a new function $G : \mathbb{N} \to \mathbb{N}$ by $G(1)=F(0), G(2)=F(1), G(3)=F(1)+F(2),$ and in general $$G(n)= F(0)+F(1)+F(2)+ \cdots +F(n-1), \, \forall \, n \geq 2.$$ We have the following two statements: \begin{enumerate}[(a)] \item For all $n \geq 2$, we have $G(n+1)-G(n) = F(n).$ \item For $n \geq 2$, we have the inequality $G(n+1) \le G(n) + F(1).$ \end{enumerate} Which of the following statements is true about function F and function G?[/INST]