Descartes sets out to discover if any ideas by being in the self guarantee that what they represent exists outside the self. what idea does guarantee that its referent exists outside the self?

The idea that guarantee that it's referent exist outside the self is : an innate idea.

Explanation:

Descartes described three ideas: adventitious, innate, invented. The one of them that is a garantee that  referent exist outside the self is innate.

This idea according to Descartes, id born in a human, it is not learned for experience. God for instance would correspond to a innate idea. He explains that the body is a continuant of God. If there is an idea of God, there referent of it is outside.

GOD, Innate (internal)

Explanation:

Descartes in his contribution to the mind philosophy, explains the innate self and the instincts of a human being.

Here he observed that since a man carries the idea of "God" innately(from birth) ,God therefore exists.