Below is the list of tables from the database along with their columns and datatype. Need to generate an accurate SQL query for the question.
Only use the columns present in the respective table. Only use the columns which are required to generate the SQL query. Only use table joins if required and not otherwise.

### Tables ###
TABLE: CREATE TABLE problems ( reported_by_staff_id VARCHAR, closure_authorised_by_staff_id VARCHAR )
TABLE: CREATE TABLE staff ( staff_id VARCHAR, staff_first_name VARCHAR, staff_last_name VARCHAR )

### Question ###
What are the product ids for the problems reported by Christop Berge with closure authorised by Ashley Medhurst?

### Accurate SQL ###

SELECT product_id FROM problems AS T1 JOIN staff AS T2 ON T1.reported_by_staff_id = T2.staff_id WHERE T2.staff_first_name = "Christop" AND T2.staff_last_name = "Berge" INTERSECT SELECT product_id FROM problems AS T1 JOIN staff AS T2 ON T1.closure_authorised_by_staff_id = T2.staff_id WHERE T2.staff_first_name = "Ashley" AND T2.staff_last_name = "Medhurst"