Transfer from Shinkansen to the Odoriko at Tokyo Station

Hi,

I will be reserving tickets and seats on the same day for YONEZAWA - TOKYO - ITO (7 Dec 2024)
The JR East website allows me to book (1) Yonezawa to Tokyo on the shinkansen and (2) Tokyo to Ito on the Odoriko. There is no through ticket from Yonezawa to Ito.
When we arrive at Tokyo station from Yonezawa, which tickets do we insert into the Shinkansen ticket gate?
Do we need to get out of the station and go in again for our trip from Tokyo station to Ito?
or is there a way to transfer to the Odoriko within the station after getting off the Shinkansen?

I am confused about which tickets to insert into the ticket gates once we arrive at Tokyo station from Yonezawa.

Thanks in advance.