2/3 Stroke Linkage Question

Greetings, I'm trying to reverse-engineer a machine for home use (please see attached video). I have a good grasp on the internal construction, except that the extension must be 2/3 of the total cycle (retraction being 1/3). I have a feeling this can be solved with a four-bar linkage, but I haven't spent enough time with them to know for sure. Perhaps there's another linkage I haven't considered? Any thoughts are appreciated, thanks in advance.