Sunkatathesis is the technical term for the act by which the rational faculty grants consent to an impression. A phantasia arrives; the hēgemonikon assents (or refuses); and if it assents, the proposition presented in the impression is now treated as true.
The Stoics' insistence on the specifically voluntary character of assent is the doctrinal foundation of their entire psychological ethics. Impressions arrive whether or not we will them — the propatheia, the involuntary first movement. But assent is up to us. We can refuse it. We can examine the impression first. We can grant assent provisionally. The freedom that the Stoics insist on — even the freedom of the slave Epictetus or the prisoner Socrates — is the freedom to grant or refuse assent.
This is why prosochē (continuous attention) is the foundational practice. Prosoche is what stands guard at the gate of assent. When the discipline lapses, assent is granted automatically — to flattering impressions, to alarming impressions, to whatever impression has rhetorical force. When the discipline is maintained, the gap between impression and assent stays open long enough for the rational faculty to do its work.
A practical consequence. When you find yourself in the grip of a passion — anger, fear, grief — the diagnostic question is: what proposition did I assent to that I should not have? "She did that on purpose." "This is intolerable." "I will not survive this." Find the proposition that was granted assent. That is the leak. The practice of prosochē is the practice of not granting it next time.
Epictetus, Discourses 1.28, 2.18