How to combine the Authorization\Registration\Password Recovery system in Laravel 5.2?

Question

Laravel

There is a standard Laravel 5.2 authorization system.
There is a form

<form action="{{ url('/login') }}" method="post">
        <fieldset>
            <div class="container-form">
                <h3>Войдите или зарегистрируйтесь</h3>
                <a href="#" title="tt close" class="close-popup"><strong><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 16.63 17.06"><title>close</title><path class="close-svg" d="M15.3,17.06l-7-7.16-7,7.16L0,15.73l6.95-7.2L0,1.4,1.26,0l7,7.16,7-7.2,1.33,1.33-7,7.2,7,7.2Z" style="fill:#ffffff"/></svg></strong></a>
                <div class="field-row">
                    <input name="email" type="email" value="{{ old('email') }}" class="text {{ $errors->has('email') ? ' error-input' : '' }} " id="field4" placeholder="E-mail">
                </div>
                <div class="field-row">
                    <input name="password" type="password" value="" class="text {{ $errors->has('password') ? ' error-input' : '' }}" id="field2" placeholder="Пароль">
                </div>
                <div class="row-checkbox">
                    <input type="checkbox" class="checkbox" id="field3" name="remember">
                    <label name="Remember" for="field3">Запомнить меня</label>
                </div>
                <div class="row-buttons">
                    <button type="submit" name="enter" class="button">Вход</button>
                    <button type="submit" name="register" class="button">Регистрация</button>
                </div>
                <div class="row-buttons">
                    <button type="submit" name="forgot" class="button">Забыли пароль!!?</button>
                </div>
                {{csrf_field()}}
            </div>
        </fieldset>
    </form>

It has 3 buttons with different name. How can it be combined so that when the request arrives, it does what is indicated in name.
When registering - registered, with a password.
At authorization - authorized and sent mail.
When restoring - sent an email with a link.
I'm interested in exactly how to combine all this, since the typical laravel authorization system does this with different controllers and traits, which implies sending and processing requests with different routes.

Answer 1

Make js handlers for each button.

Answer 2

Add hidden field with name and handle it in controller?