Hello. How to remove the Advanced Search?

Hi Denis,
Please go to the file: /app/design/frontend/default/jm_jasmine/layout/catalogsearch.xml find and replace the code like below:

<reference name="footer_links">
 <action method="addLink" translate="label title" module="catalogsearch" ifconfig="catalog/seo/search_terms">
 <label>Search Terms</label>
 <url helper="catalogsearch/getSearchTermUrl" />
 <title>Search Terms</title>
 </action>
 <action method="addLink" translate="label title" module="catalogsearch">
 <label>Advanced Search</label>
 <url helper="catalogsearch/getAdvancedSearchUrl" />
 <title>Advanced Search</title>
 </action>
</reference>

Replace with: 

<reference name="footer_links">
 <action method="addLink" translate="label title" module="catalogsearch">
 <label>Advanced Search</label>
 <url helper="catalogsearch/getAdvancedSearchUrl" />
 <title>Advanced Search</title>
 </action>
</reference>

It will working fine like you want. Remember clear cache from magento.
Best Regards,
Ziven.