Why reCaptcha don't work on my wordpress comments template

I'm trying to avoid spam in the comments of my first wordpress theme, and the question is that I've followed all the Google PHP API instructions, and it's showing perfectly, but the validating is going wrong, I think cause I can post comments entering wrong words in the recaptcha.

Exploiting the issue, I would also like to know how I can put the error message returned, together with the submit button.

This is the comments.php form fragment:

<form class="comments-form" action="verify.php" method="post" id="commentform">
	
           ...

	<?php
      require_once('recaptchalib.php');
      $publickey = "my_pulic_key";
      echo recaptcha_get_html($publickey, $error);
    ?>

	<p>
		<input type="submit" name="submit" id="submit" tabindex="5" value="Enviar" />
		<label for="submit"><?php echo $error ?></label>
		<input type="hidden" name="comment_post_ID" value="<?php echo $id; ?>" />
	</p>
	
	<?php do_action('comment_form', $post->ID); ?> 

</form>

And this is the verify.php code:

    <?php
      require_once('recaptchalib.php');
      $privatekey = "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"; //clave privada
      $resp = recaptcha_check_answer ($privatekey,
                                    $_SERVER["REMOTE_ADDR"],
                                    $_POST["recaptcha_challenge_field"],
                                    $_POST["recaptcha_response_field"]);

  if (!$resp->is_valid) {
    // What happens when the CAPTCHA was entered incorrectly
    $error = $resp->error;
  } else {
    // Your code here to handle a successful verification
    echo "¡Recaptcha correcto!";
    //do_action("wp-comment-post.php");??????I DON´T KNOW IF THIS IS OK.
  }
  ?>

EDIT: I've tried with the form action "verify.php" but only redirect me to an empty page. Which is the correct action that I should use?