I provided you with a working zip file, it wouldn't kill you to take some time and try debug yourself, maybe start by adding something like
var_dump($_POST);
die();
At the top of your action_page.php then submit the form until you sort your fields out...
Firstly you're missing the `method` attribute on your form.
Secondly all the input names do not match the POST values you're expecting on the PHP side.
Have attached the fixed version.