Finding a verb analogous to 'analyse' (US 'analyze') requiring complementiser

I’m proofreading an academic paper and have come across the following:

"This process, as Smith analyses, is a way to reflect on…"

Intuitively I’d prefer

"This process, as Smith explains/says/states, is a way to…’

I’ve come to the (possibly wrong) conclusion that it’s somehow because these verbs can take ‘that’ as a complementiser/conjunction (or in the case of ‘says’, take a null complementiser):

"Smith says that it’s possible…"/"Smith says it’s possible…"

"Smith explains that…"

"Smith states that…"

While ‘analyse’ is a bit murkier to me:

?"Smith analyses that it’s possible…"

However, I also think that ‘analyse’ bears a different semantic weight to ‘say/state/explain’, and I’d really like to keep (at least some of) its meaning, rather than just evade all this and change to ‘say/state/explain’. I’ve tried substituting ‘explore’, ‘investigate’ and ‘discuss’ but I’m not sure that I’m not running up against the same problem with each of them. So my question, in two parts, is:
a) Is my intuitive preference actually legit, or should I not worry about it and accept "as Smith analyses"?
b) If my intuition is legit, is there a verb that acts structurally like one of those verbs that takes ‘that’, while remaining similar to the meaning of ‘analyse’? Are ‘explore/investigate/discuss’ perhaps more satisfactory?

Apologies if this is a duplicate question – I made a few searches but wasn’t sure how to frame the keywords, so was unsuccessful. Annoyingly I feel sure that I’ve come across this in my work before, but can’t remember how/if I resolved it at the time…