Let $a, b, c$ be positive real numbers. Prove that $$\frac{1}{2a+\frac{1}{abc}+1}+\frac{1}{2b+\frac{1}{abc}+1}+\frac{1}{2c+\frac{1}{abc}+1}\le \frac{a + b + c}{a+b+c+1}$$$$\frac{1}{a+\frac{1}{abc}+2}+\frac{1}{b+\frac{1}{abc}+2}+\frac{1}{c+\frac{1}{abc}+2}\le \frac{3(a + b + c)}{2(a+b+c+3)}$$