WordPress Nonce Verify Not Working on Login With Ajax

Question

I want to use WordPress Nonce to verify LogIn form. It not working. My form and Ajax code on Login page And validation on Another page.

HTML

<form id="frmLogin">

<?php wp_nonce_field('test_action', 'submit_post'); ?>
                      
<input type="text" id="InputName" maxlength="150" class="form-control" name="username" required />
<input type="password" id="InputPassword" maxlength="150" class="form-control" name="password" required />
<input type="submit" maxlength="150" class="form-control form-control-lg bg-warning" name="submit" value="Login" />                 
</form>


// LogIn Validation on Another PHP page

add_action( 'wp_ajax_nopriv_login_data', 'ajax_login_data' );
function ajax_login_data(){
    $login_array = [];
    wp_parse_str($_POST['login_data'], $login_array );


// Nonce Verify
if(wp_verify_nonce($_REQUEST['test_action'], 'submit_post')){
           /// do your work
  }else{
         /// throw an error
  }

}

Please help me to solve this problem.