A four-variable cyclic quadratic reciprocal sum bounds the total

Given $a, b, c, d > 0, \ \ \ \frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{d}+\frac{d^2}{a} \ge a+b+c+d$ . Prove that this is true by Rearrangement inequality.

Source: InternLM Lean-Workbook, record lean_workbook_1454 (Apache-2.0). Complete source proposition preserved; proof developed independently.