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 Problem_Log ( problem_log_id INTEGER, assigned_to_staff_id INTEGER, problem_id INTEGER, problem_category_code VARCHAR(20), problem_status_code VARCHAR(20), log_entry_date DATETIME, log_entry_description VARCHAR(255), log_entry_fix VARCHAR(255), other_log_details VARCHAR(255) )
TABLE: CREATE TABLE Problems ( problem_id INTEGER, product_id INTEGER, closure_authorised_by_staff_id INTEGER, reported_by_staff_id INTEGER, date_problem_reported DATETIME, date_problem_closed DATETIME, problem_description VARCHAR(255), other_problem_details VARCHAR(255) )
TABLE: CREATE TABLE Product ( product_id INTEGER, product_name VARCHAR(80), product_details VARCHAR(255) )
TABLE: CREATE TABLE Problem_Category_Codes ( problem_category_code VARCHAR(20), problem_category_description VARCHAR(80) )
TABLE: CREATE TABLE Staff ( staff_id INTEGER, staff_first_name VARCHAR(80), staff_last_name VARCHAR(80), other_staff_details VARCHAR(255) )
TABLE: CREATE TABLE Problem_Status_Codes ( problem_status_code VARCHAR(20), problem_status_description VARCHAR(80) )

### Question ###
What are the products that have problems reported after 1986-11-13? Give me the product id and the count of problems reported after 1986-11-13. Visualize by scatter chart.

### Accurate SQL ###

SELECT COUNT(*), T1.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