Individual Teshuvah, With the Community

Teshuva requires that a person make an honest assessment of his spiritual standing. To do this, it would seem ideal to isolate oneself from all distractions, to focus on one’s past deeds. Why do we see, that on Yom Kippur – the main day for Teshuvah of the whole year – we spend the entire day in a public place, in synagogue, together with so many others?