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 product (product_id VARCHAR)
TABLE: CREATE TABLE problems (product_id VARCHAR, date_problem_reported INTEGER)

### Question ###
For each product that has problems, find the number of problems reported after 1986-11-13 and the product id?

### Accurate SQL ###

SELECT COUNT(*), T2.product_id FROM problems AS T1 JOIN product AS T2 ON T1.product_id = T2.product_id WHERE T1.date_problem_reported > "1986-11-13" GROUP BY T2.product_id