I cant seeem to get this form to work, currently it acts as though its working but not recieving any mail?

<form method="post" action="action_page.php" novalidate>
        <label for="name">Name</label>
        <input name="name" id="name" type="text" required>

        <label for="email">Email</label>
        <input name="email" id="email" type="email" required>

        <label for="message">Message</label>
        <textarea name="message" id="message" placeholder="" required></textarea>

        <div id="important">
            <label for="human">What is 2+2?</label>
            <input name="human" id="human" placeholder="">
        </div>

        <div id="contact-footer">
            <p>Your email address will only be used to reply to your message and
                your personal information
                will never be shared.</p>
        </div>

        <div id="form-flex">
            <div class="g-recaptcha-con">
                <div class="g-recaptcha" data-sitekey="6Ldkew0qAAAAAMQHlmn177hTXLtVcZ9fkmVxLqqL"></div>
            </div>
            <div class="submit-div">
                <input type="submit" id="submit" class="button" name="submit" value="Send Message">
            </div>
        </div>
    </form>

<?php
if (isset($_POST['submit'])) {
    // reCAPTCHA validation
    if (isset($_POST['g-recaptcha-response']) && !empty($_POST['g-recaptcha-response'])) {
        // Google secret API key
        $secretAPIkey = '6Ldkew0qAAAAANFhvgiOKViu_tduZTncnXJ8dRXi';

        // reCAPTCHA response verification
        $verifyResponse = file_get_contents('https://www.google.com/recaptcha/api/siteverify?secret=' . $secretAPIkey . '&response=' . $_POST['g-recaptcha-response']);
        $responseData = json_decode($verifyResponse);

        if ($responseData->success) {
            // Check if the anti-spam field is filled
            if (!empty($_POST['human'])) {
                // If the anti-spam field is filled, consider it spam and don't send the email
                echo "<h2>Spam detected!</h2>";
                echo "<p>Your message has been flagged as spam and not sent.</p>";
            } else {
                // Send email
                $name = $_POST['name'];
                $email = $_POST['email'];
                $message = $_POST['message'];
                $to = '[email protected]';
                $subject = 'Message';

                $headers = "From: $emailrn";
                $headers .= "MIME-Version: 1.0rn";
                $headers .= "Content-type: text/html; charset=iso-8859-1rn";

                $body = "From: $namern";
                $body .= "E-Mail: $emailrn";
                $body .= "Message:rn $message";

                if (mail($to, $subject, $body, $headers)) {
                    echo '<p>Your message has been sent successfully!</p>';
                } else {
                    echo '<p>Something went wrong, go back and try again!</p>';
                }
            }
        } else {
            echo '<p>reCAPTCHA verification failed. Please try again.</p>';
        }
    } else {
        echo '<p>Please complete the reCAPTCHA.</p>';
    }
} else {
    echo '<p>Form not submitted properly.</p>';
}
?>

At firt the recaptcha check was in the wrong place and the form was sending without having to complete it, I changed it to check recapcha first before processing the rest of the form, now it takes me to action_page.php as though its sent but I am not recieiving any mail now, it was before.