A component isn't the same as a model. So if you want to do things this way, you'll have to turn your
Action model into a Component.
The component would go into
Controller/Component/ActionComponent.php, and then it can be included into your Controllers like this:
public $components = array(..., 'Action');
The logic in your Component can be similar to that in a Model, but there are some differences. For example, you could still have an Action model, and the component can use that for CRUD and other stuff. You'll have to use
ClassRegistry::init() to load a model into your Component though.
I can't really explain how to do exactly what you want, one reason for that being that I don't know precisely enough what it is you do want. However, I've written my own Component before and you can use it for reference if you like - it's possibly more complicated than yours so you can see how to write methods for it.
In that example, once it's included in a Controller, I can simply call
$this->CustomAcl->check() anywhere I like.
I hope this is enough to get you started at least.