Final answer:
In the three stages of cooking, starches undergo the final 'cooling' stage which solidifies the thickened mixture into a gel-like consistency.
Step-by-step explanation:
The third stage that starches go through in cooking is cooling, which solidifies the thickened mixture. During the cooking process, starch undergoes a transition called gelatinization, where heat causes starch granules to swell as they absorb water, consequently breaking down and resulting in a thickened mixture. Upon cooling, this mixture sets and forms a gel-like structure, due to the organization of the starch into a complex three-dimensional network that traps water molecules, creating a firm, gelatinous mass.