How do I use the / (index) route twice for both logged in and logged out?

I'm working on a Laravel project. The project has a public (non authenticated section of the site) and an authenticated section (admin).

I am attempting to use the / route to display a public homepage view, and then when authenticated I'd like the same / route to display the admin authenticated view.

This is the attempted code:

routes.php

Route::auth();

Route::get('/', function () {
        return view('Public.home');
    });

Route::group(['middleware' => ['auth']], function () { 

    Route::get('/', function () {
        return view('Authenticated.home');
    });
});

Problem When I am logged out and try to access the / route, the Public controller (Public.home) is considered as an authenticated route (as placed under the 'auth' middleware in the route group above).

The middleware auth is set to redirect to / when any protected (authenticated) routes are accessed.

Authenticate.php

<?php

namespace App\Http\Middleware;

use Closure;
use Illuminate\Support\Facades\Auth;

class Authenticate
{
    /**
     * Handle an incoming request.
     *
     * @param  \Illuminate\Http\Request  $request
     * @param  \Closure  $next
     * @param  string|null  $guard
     * @return mixed
     */
    public function handle($request, Closure $next, $guard = null)
    {
        if (Auth::guard($guard)->guest()) {
            if ($request->ajax() || $request->wantsJson()) {
                return response('Unauthorized.', 401);
            }

            return redirect()->guest('/');
        }

        return $next($request);
    }
}

I am using Laravel 5.2.

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