profecto

Profecto is an adverb frozen out of pro facto, "for a fact", and that is exactly what it means: certainly, assuredly. It is emphatic and a little formal, at home in oratory and in Livy, and it modifies the whole statement rather than any one word in it.

The trap is parsing, not sense. Profecto is also the dative and ablative singular of profectus, the perfect participle of proficiscor, so the same eight letters can be "assuredly" or "having set out". Position settles it: the adverb usually sits early in its clause with no noun to agree with, while the participle is anchored to one.