$\forall(a\_1,...,a\_n),(b\_1,...,b\_n)\in\mathbb R^n$, How to deduce the Cauchy–Schwarz inequality from this inequality : $$\sum\_{k=1}^{n}|a\_kb\_k|\le\frac{1}{2}\left(\sum\_{k=1}^{n}a\_k^2+\sum\_{k=1}^{n}b\_k^2\right)$$

I recall that the Cauchy–Schwarz inequality is :$$\left(\sum\_{k=1}^{n}a\_kb\_k\right)^2\le\left(\sum\_{k=1}^{n}a\_k^2\right)\left(\sum\_{k=1}^{n}b\_k^2\right)$$