Halliday & Matthiessen (2014: 576-7):
The extending complex is a two-part process, in which the Subject fills a dual participant role: Behaver (in the conative component) plus Actor, or some other role, in the happening itself. For the same reason, Adjuncts in the clause may relate semantically to the conative component like hard, quickly in she tried hard to write well, she quickly learnt to tell them apart.The Filipino tried hard to put in a storming finish, but his attacks were nearly all neatly countered by the clever champion.
There is no need in the analysis to tie these structurally to the primary verbal group; but it is useful to specify their function, by labelling them as ‘conative Adjunct’.