Get a random thumbnail from posts belonging to a specific taxonomy

So in order to do this, I needed to first do a for each loop, store the category slug as a variable, JAMterm, and then use that in a query to pull one random thumbnail from the category.

Thanks to @Renishkhunt for helping me along the way to get this answer.

<?php
    $taxonomyName = "category";
    $terms = get_terms($taxonomyName,array('parent' => 79));
    echo '<ul>';
    foreach($terms as $term) {
        echo '<li><a href="'.get_term_link($term->slug,$taxonomyName).'">'.$term->name.'</a><br/>';

        $JAMterm = $term->slug;

        global $wp_query;
        $term = $wp_query->queried_object;

        $args=array(
            'orderby' => 'rand',
            'posts_per_page' => 1,
            'post_type' => 'post',
            'tax_query' => array(
                array(
                    'taxonomy' => 'category', 
                    'field' => 'slug', 
                    'terms' =>  $JAMterm
                )
            )
        );

        $new_query = null;
        $new_query = new WP_Query($args);

        while ($new_query->have_posts()) : $new_query->the_post();
            the_post_thumbnail(); 
        endwhile;
        wp_reset_postdata();


        echo '</li>';
        }
    echo '</ul>';
?>