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 table_name_65 (bronze INTEGER, total VARCHAR, rank VARCHAR)

### Question ###
What is the average number of bronze medals won among nations that won at least 1 medal and are not ranked 1st?

### Accurate SQL ###

SELECT AVG(bronze) FROM table_name_65 WHERE total > 1 AND rank > 1