How to include another jsp page from custom jsp tag

I want to have a custom Jsp tag with one string attribute, if this is a a path to another jsp file then I want to include that JSP in the page (behave as a jsp:include); if not, then I want to just output the string in the body of the page.

I don't know how to do the jsp:include part...

I see there's a setJspBody in SimpleTagSupport that I can pass a JspFragment... But I don't know how to get that... I was hoping to find something like an IncludeTag class in javax.servlet.jsp that I could just delegate this logic to, like so setJspBody( new IncludeTag(...).getJspFragment() ) but I don't find what class implements the jsp:include functionality in the docs.

I used PageContext.include

public class MyIncludeTag extends TagSupport {
   private String page;
   //getters setters
   @Override
   public int doStartTag() throws JspException {
     try {
            pageContext.include(page);
        } catch (ServletException | IOException e) {
            throw new JspException("Failed to include " + page, e);
        }
        return super.doStartTag();
   }
}