Laravel Breez and Spatie Permissions set role while user registered

I'm using laravel Breez as Auth scaffolding package by laravel and I setup laravel permissions by spatie.

I have created two registration forms one for "Writer" and other for "Publisher" all registration views are located in RegisteredUserController

app\Http\Controllers\Auth\RegisteredUserController.php

<?php

namespace App\Http\Controllers\Auth;

use App\Http\Controllers\Controller;
use App\Models\Frontend\User;
use App\Providers\RouteServiceProvider;
use Illuminate\Auth\Events\Registered;
use Illuminate\Http\Request;
use Illuminate\Support\Facades\Auth;
use Illuminate\Support\Facades\Hash;

class RegisteredUserController extends Controller
{
    /**
     * Display the registration view for writer.
     *
     * @return \Illuminate\View\View
     */
    public function createWriter()
    {
        return view('auth.writer.writer-space');
    }
    
    /**
     * Display the registration view for publisher.
     *
     * @return \Illuminate\View\View
     */
    public function createPublisher()
    {
        return view('auth.publisher.publisher-space');
    }

    /**
     * Handle an incoming registration request.
     *
     * @param  \Illuminate\Http\Request  $request
     * @return \Illuminate\Http\RedirectResponse
     *
     * @throws \Illuminate\Validation\ValidationException
     */
    public function store(Request $request)
    {
        $request->validate([
            'name' => 'required|string|max:255',
            'email' => 'required|string|email|max:255|unique:users',
            'password' => 'required|string|confirmed|min:8',
        ]);

        Auth::login($user = User::create([
            'name' => $request->name,
            'email' => $request->email,
            'password' => Hash::make($request->password),
        ]));

        event(new Registered($user));

        return redirect(RouteServiceProvider::HOME);
    }
}

as you can see in this controller I have two registration view for two type of users "Writer" and "Publisher".

What I want to do is to Set the role of the users while registration based on this two types "Writer" and "Publisher" Roles using laravel-permission by spatie.

app\routes\auth.php

<?php

use Illuminate\Support\Facades\Route;
use App\Http\Controllers\Auth\RegisteredUserController;

Route::get('/publisher-space', [RegisteredUserController::class, 'createPublisher'])->middleware('guest')->name('publisher-space');

Route::get('/writer-space', [RegisteredUserController::class, 'createWriter'])->middleware('guest')->name('writer-space');