update and insert triggers in sqlite

I want to have riggers that set the last_modified column automatically each time a row in updated or inserted. Lets say I have an ID that is unique to each row.

This is my query:

CREATE TRIGGER insert_trigger
AFTER INSERT ON TABLE_NAME

BEGIN

update TABLE_NAME set last_modified =strftime('%Y-%m-%d %H:%M:%S:%s','now', 'localtime') where id = old.id;

END;

After creating this trigger, when I try to insert I get the error:

no such column: old.id

I can understand why I get this error, but how can I create a proper trigger?