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Custom Taxonomy Search result page

I have a post type named Icons,
I have a custom taxonomy named Icons Pack which have a custom field for featured image.
Also I have a search form in my site for users to search for the icons they want to find. The form also have a checkbox named "search in packs".
What I’m trying to achieve is when users check this checkbox, the search result page must be a page that lists all the icon packages(list of custom taxonomy terms) for the searched keyword, and If users didn’t check the checkbox, show them a different search result page template.

Is there any way to do this?