cookies & caching

I have a page that depends on cookies to be rendered properly. Something like this:

<?php if isset(($_COOKIE['_clientInfo'])) { ?>

   <p>You have the cookie, so put in your logical stuff here and load the document as you will.</p>

<?php } else { ?>

   <p>You don't have the cookie yet, so don't load anything but the resources you need to test the client and set the cookie. Then refresh.</p>

<?php } ?>

As you can imagine this is not working properly with WP Super Cache on. Any advice how to solve the problem?

https://ww.wp.xz.cn/plugins/wp-super-cache/