To render a foreign action output inside the view that belongs to your current action, you need to call the foreign action from your current action, then store its output to a variable and pass it to your current view.
Calling actions from the same controller
If the action you want to render is inside the same controller you are using, you could call:
$result = $this->action();
return view('my.view',['my_rendered_action'=>$result]);
And then, inside your view, just:
{!! $my_rendered_action !!}
Take care of not rendering anything that comes from the user using this method, because {!! !!} tags won't scape dangerous inputs. If you do not need to have HTML inside your action response, always prefer using {{ }} instead.
Calling actions from another controller
If you need to share a method between more than one controller, the cleanest way is to create a trait or a Job that implements the logic, and then both controllers would use the trait or dispatch the same job.
Please refer to Shaddy's answer to this question for more information.
Hope it helps. ;)