Range of Reverse Regression Slope Given Forward Slope

Consider two regressions on centered data (zero-intercept): - Regress $y$ on $x$: $y \sim bx$, with OLS slope $b = \text{Cov}(x,y) / \text{Var}(x)$ - Regress $x$ on $y$: $x \sim cy$, with OLS slope $c = \text{Cov}(x,y) / \text{Var}(y)$ Given that $b = 1$, determine the range of possible values for $c$. Include detailed steps and reasoning.