You need to nest <ui:param> inside <ui:include> to pass parameters to the included file.
<ui:include src="https://stackoverflow.com/questions/5291181/general.xhtml">
<ui:param name="action" value="actionOne" />
</ui:include>
and in the include:
<h:commandButton action="#{action}" />
Note that this only supports strings, not action methods. For the latter you would need to upgrade to JSF 2.0 and use composite components.