Formally, this reaction is unbalanced, therefore some information is missing. The terminal acetylenic carbon has the oxidation state of a carboxylic acid or ester. Cyclization should be more easily accomplished at that stage. If the reaction were to follow that path then a mineral acid and/or mercury salts could catalyze it.
It could be possible for the amine to add to the acetylene, and then a Cope-like electrocyclic elimination of ethylene. I would not expect this mechanism unless this mechanism has been discussed in class (which I skipped).