new variable created in mytheme_preprocess_node not available in mytheme_preprocess_page

Hi,
I am working on preparing a theme which has a tabs structure. Tabs are made with Jquery. It requires a special structure. I am trying to chive that structure. Till now I have prepared divs, but not been able to prepare ul-li structure.

This is how I am been working, I prepared a function in template.php called mytheme_preprocess_node ()

function mytheme_preprocess_node (&$vars) {
    $node = $vars['node'];
    if ($node->type == "tab_content") {
        $vars['ul_data'] = "<li><a href='#". strtolower(str_replace(" ", "-", $node->title)) ."'>". $node->title ."</a></li>";
    }
}

I created a $ul_data variable, this variable I can access in node.tpl.php, but not in main page.tpl.php and in mytheme_preprocess_page.
I want that variable in page.tpl.php, So as to print ul-li structure.

Am I doing it right?